Discrete Symmetries on the Light Front and a General Relation Connecting Nucleon Electric D

Never giving up is a principle that can be applied to various aspects of life,from personal growth to professional achievements.Here are some key points to consider when writing an essay on the importance of perseverance in English:1.Introduction:Begin by defining what it means to never give up.You could start with a quote or a story that illustrates the concept of perseverance.2.Importance of Perseverance:Discuss why it is essential to keep going even when faced with challenges.This could include the development of resilience,the satisfaction of overcoming obstacles,and the potential for growth and learning.3.Examples of Perseverance:Historical Figures:Mention individuals like Thomas Edison,who failed numerous times before inventing the light bulb,or Abraham Lincoln,who faced numerous defeats before becoming the President of the United States.Athletes:Cite examples of athletes who have overcome injuries or setbacks to achieve success,such as Michael Jordan,who was cut from his high school basketball team but went on to become one of the greatest players in history.4.Personal Stories:Share personal anecdotes or experiences where perseverance led to success.This could be a personal achievement or a situation where you witnessed someone elses determination pay off.5.Strategies for Perseverance:Setting Goals:Explain how setting realistic and achievable goals can help maintain motivation.Developing a Growth Mindset:Discuss the concept of a growth mindset and how it can foster resilience in the face of failure.Seeking Support:Mention the importance of having a support system,such as friends, family,or mentors,who can provide encouragement and advice.6.Overcoming Failure:Address the fear of failure and how it can be a stepping stone to success.Discuss how learning from mistakes and viewing them as opportunities for growth can be beneficial.7.The Power of Persistence:Highlight the psychological benefits of persistence,such as increased selfconfidence and a sense of accomplishment.8.Conclusion:Summarize the main points of your essay and reiterate the importance of never giving up.End with a call to action,encouraging readers to adopt a perseveringattitude in their own lives.nguage and Style:Use a variety of sentence structures and vocabulary to convey your message effectively.Emphasize the positive connotations of perseverance and the negative implications of giving up.10.Revision and Editing:After writing the first draft,revise your essay for clarity, coherence,and grammatical accuracy.Ensure that your essay flows logically and that each paragraph contributes to the overall argument.Remember,an essay on never giving up should inspire and motivate readers to face their challenges with determination and a positive e concrete examples and a compelling narrative to make your essay engaging and memorable.。

徜徉于天人之间天人之间最近杨振宁教授和翁帆女士合作的《曙光集》出版，里面收集了将近五十篇杨先生的文章、书信、访问记，以及数篇与他相关的文字，其中关于科学与科学家的大约占六成，关于历史、文化、中国现状和前景的占四成，从中可以窥见这位物理学大师过去三十年间对物理学基本理论的反思、对前辈和朋侪的情谊，以及对国家民族前途的关怀。

对于像我这样从物理学转到文史领域的中国知识分子来说，阅读此集正有如孙髯翁所谓“五百里滇池奔来眼底，数千年往事注到心头”，一时间赞叹、惊讶、迷思、感慨交集。

更何况，我有幸认识杨先生多年，为这些散乱思绪做个记录，对个人，对读者应该都是有意义的。

世中遥望空云山物理学的终极追求是从自然界万象中找出基本规律。

这从古希腊的自然哲学开始，到欧几里得的《几何原本》而获得第一个突破，两千年后牛顿的《自然哲学之数学原理》带来第二个突破，至于二十世纪初的相对论和量子力学之发现则已经是第三次突破了。

这三次突破或曰“科学革命”代表人类认知模式之根本变革。

杨先生因缘际会，刚好赶上参加第三次科学革命的后续阶段，以是得成大学问。

《曙光集》中讨论“分立对称性”(discrete symmetries)、“规范场”(gauge field)和统计物理学发展史的十来篇文章便是他躬与其役的现身说法。

其中《爱因斯坦对理论物理的影响》、《分立对称性P,T和C（附报告后的讨论）》和《魏尔对物理学的贡献》等三篇更将他自己的思想历程与贡献放在前人工作与基本理论整体发展的大背景中来讨论，那是非常深刻和有味道的科学史料，但对于此专门领域以外的读者而言，则恐怕有如隔雾看花，难免“世中遥望空云山”之叹。

当然，这是无可奈何的。

理论物理学之所以精确、奥妙，是因为它建立在数学语言而非自然语言之上，这也就是斯诺(C.P. Snow)所谓“两种文化”之间的鸿沟。

柏拉图在《对话录》(The Dialogues)的《米诺篇》(Meno)中通过与童奴问答来说明，正方形面积加倍时，其边长等于原正方形的对角线，而并非原边长的双倍。

读后续写技能训：修辞改装法（解析版）目录Part 1修辞改装法 (1)第一种修辞：比喻 (2)第二种修辞：拟人 (7)第三种修辞：夸张 (10)其他修辞法： (11)Part 2 翻译练习 (17)（第一组） (17)（第二组） (18)（第三组） (18)（第四组） (19)（第五组） (19)（第六组） (20)翻译练习答案 (21)Part 3 综合演练【模拟题】 (22)1．读后续写模拟专练 (22)2．（2022.湖南.一模） (26)3．（2022.辽宁大连.模拟预测） (28)Part 1修辞改装法今天我要分享的主题是：如何用三种修辞手法来升级我们的句子。

适当的修辞可以让我们的句子增光添彩。

试着比较一下，下面两个句子：第1个句子：Jenny was very happy. （Jenny很开心。

）第2个句子：Jenny couldn't resist her inner joy, flying into the door like a bird.（Jenny控制不住内心的喜悦，像小鸟一样飞进了家门。

）是不是感觉第二个用了比喻后，Jenny开心的画面跃然纸上，非常生动。

今天我们这节课，就学习简单的几个修辞手法的技巧，分别是比喻，拟人和夸张。

这三种在我们的读后续写中，用的较多。

第一种修辞：比喻(1)Simile明喻俗称直喻，是依据比喻和被比喻两种不同事物的相似关系而构成的修辞格。

如：1.The country, covered with cherry tree flowers, looks as though it is coveredwith pink snow.开满樱花的乡村，看起来有如粉红雪铺满地。

2.The smile on her face shone like a diamond.她的笑容像宝石一样闪闪发光。

3.The scenery along the Lijiang River in Guilin is just like abeautiful landscape painting.桂林漓江的沿途风景就像一幅美丽的山水画。

More informationFundamentals of Photonic Crystal GuidingIf you’re looking to understand photonic crystals,this systematic,rigorous,and peda-gogical introduction is a must.Here you’llfind intuitive analytical and semi-analyticalmodels applied to complex and practically relevant photonic crystal structures.Y ou willalso be shown how to use various analytical methods borrowed from quantum mechanics,such as perturbation theory,asymptotic analysis,and group theory,to investigate manyof the limiting properties of photonic crystals,which are otherwise difficult to rationalizeusing only numerical simulations.An introductory review of nonlinear guiding in photonic lattices is also presented,as are the fabrication and application of photonic crystals.In addition,end-of-chapterexercise problems with detailed analytical and numerical solutions allow you to monitoryour understanding of the material presented.This accessible text is ideal for researchersand graduate students studying photonic crystals in departments of electrical engineering,physics,applied physics,and mathematics.Maksim Skorobogatiy is Professor and Canada Research Chair in Photonic Crystals atthe Department of Engineering Physics in´Ecole Polytechnique de Montr´e al,Canada.In2005he was awarded a fellowship from the Japanese Society for Promotion of Science,and he is a member of the Optical Society of America.Jianke Yang is Professor of Applied Mathematics at the University of Vermont,USA.Heis a member of the Optical Society of America and the Society of Industrial and AppliedMathematics.Fundamentals of Photonic Crystal GuidingMAKSIM SKOROBOGATIY 1JIANKE YANG 2´Ecole Polytechnique de Montr ´e al,Canada 1University of Vermont,USA2More informationMore informationcambridge university pressCambridge,New Y ork,Melbourne,Madrid,Cape Town,Singapore,S˜a o Paulo,DelhiCambridge University PressThe Edinburgh Building,Cambridge CB28RU,UKPublished in the United States of America by Cambridge University Press,New Y orkInformation on this title:/9780521513289C Cambridge University Press2009This publication is in copyright.Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University Press.First published2009Printed in the United Kingdom at the University Press,CambridgeA catalog record for this publication is available from the British LibraryLibrary of Congress Cataloging in Publication dataSkorobogatiy,Maksim,1974–Fundamentals of photonic crystal guiding/by Maksim Skorobogatiy and Jianke Y ang.p.cm.Includes index.ISBN978-0-521-51328-91.Photonic crystals.I.Y ang,Jianke.II.Title.QD924.S562008621.36–dc222008033576ISBN978-0-521-51328-9hardbackCambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication,and does not guarantee that any content on suchwebsites is,or will remain,accurate or appropriate.More informationM.Skorobogatiy dedicates this book to his family.He thanks his parentsAlexander and Tetyana for never-ceasing support,encouragement,andparticipation in all his endeavors.He also thanks his wife Olga,his children,Alexander junior and Anastasia,andhis parents for their unconditional love.J.Yang dedicates this book to his family.More informationContentsPreface page xiAcknowledgements xii1Introduction11.1Fabrication of photonic crystals21.2Application of photonic crystals41.2.1Photonic crystals as low-loss mirrors:photonicbandgap effects41.2.2Photonic crystals for out-of-bandgap operation10References112Hamiltonian formulation of Maxwell’s equations(frequency consideration)142.1Plane-wave solution for uniform dielectrics162.2Methods of quantum mechanics in electromagnetism182.2.1Orthogonality of eigenstates192.2.2Variational principle202.2.3Equivalence between the eigenstates of twocommuting Hamiltonians222.2.4Eigenstates of the operators of continuous anddiscrete translations and rotations232.3Properties of the harmonic modes of Maxwell’s equations302.3.1Orthogonality of electromagnetic modes322.3.2Eigenvalues and the variational principle322.3.3Absence of the fundamental length scale in Maxwell’sequations342.4Symmetries of electromagnetic eigenmodes352.4.1Time-reversal symmetry352.4.2Definition of the operators of translation and rotation352.4.3Continuous translational and rotational symmetries382.4.4Band diagrams432.4.5Discrete translational and rotational symmetries44More informationviii Contents2.4.6Discrete translational symmetry and discreterotational symmetry522.4.7Inversion symmetry,mirror symmetry,and other symmetries532.5Problems553One-dimensional photonic crystals–multilayer stacks593.1Transfer matrix technique593.1.1Multilayer stack,TE polarization593.1.2Multilayer stack,TM polarization613.1.3Boundary conditions623.2Reflection from afinite multilayer(dielectric mirror)633.3Reflection from a semi-infinite multilayer(dielectricphotonic crystal mirror)643.3.1Omnidirectional reflectors I683.4Guiding in afinite multilayer(planar dielectric waveguide)693.5Guiding in the interior of an infinitely periodic multilayer703.5.1Omnidirectional reflectors II803.6Defect states in a perturbed periodic multilayer:planarphotonic crystal waveguides823.7Problems864Bandgap guidance in planar photonic crystal waveguides934.1Design considerations of waveguides with infinitelyperiodic reflectors934.2Fundamental TE mode of a waveguide with infinitelyperiodic reflector964.3Infinitely periodic reflectors,field distribution in TM modes984.3.1Case of the core dielectric constantεc<εhεl/(εh+εl)984.3.2Case of the core dielectric constantεl≥εc>εhεl/(εh+εl)1014.4Perturbation theory for Maxwell’s equations,frequencyformulation1034.4.1Accounting for the absorption losses of the waveguidematerials:calculation of the modal lifetime and decay length1044.5Perturbative calculation of the modal radiation loss in aphotonic bandgap waveguide with afinite reflector1064.5.1Physical approach1064.5.2Mathematical approach1085Hamiltonian formulation of Maxwell’s equations for waveguides(propagation-constant consideration)1105.1Eigenstates of a waveguide in Hamiltonian formulation1105.1.1Orthogonality relation between the modes of a waveguide madeof lossless dielectrics111More informationContents ix5.1.2Expressions for the modal phase velocity1145.1.3Expressions for the modal group velocity1145.1.4Orthogonality relation between the modes of a waveguide madeof lossy dielectrics1155.2Perturbation theory for uniform variations in a waveguide dielectric profile1165.2.1Perturbation theory for the nondegenerate modes:example ofmaterial absorption1185.2.2Perturbation theory for the degenerate modes coupled byperturbation:example of polarization-mode dispersion1205.2.3Perturbations that change the positions of dielectric interfaces1235.3Problems126References127 6Two-dimensional photonic crystals1296.1T wo-dimensional photonic crystals with diminishingly smallindex contrast1296.2Plane-wave expansion method1326.2.1Calculation of the modal group velocity1346.2.2Plane-wave method in2D1346.2.3Calculation of the group velocity in the case of2Dphotonic crystals1356.2.4Perturbative formulation for the photonic crystallattices with small refractive index contrast1386.2.5Photonic crystal lattices with high-refractive-index contrast1426.3Comparison between various projected band diagrams1426.4Dispersion relation at a band edge,density of states andVan Hove singularities1446.5Refraction from photonic crystals1476.6Defects in a2D photonic crystal lattice1486.6.1Line defects1486.6.2Point defects1586.7Problems167References171 7Quasi-2D photonic crystals1727.1Photonic crystalfibers1727.1.1Plane-wave expansion method1727.1.2Band diagram of modes of a photonic crystalfiber1767.2Optically induced photonic lattices1777.2.1Light propagation in low-index-contrast periodicphotonic lattices1787.2.2Defect modes in2D photonic lattices with localized defects1817.2.3Bandgap structure and diffraction relation for the modes of auniform lattice182More informationx Contents7.2.4Bifurcations of the defect modes from Bloch band edges forlocalized weak defects1857.2.5Dependence of the defect modes on the strength oflocalized defects1887.2.6Defect modes in2D photonic lattices with nonlocalized defects1927.3Photonic-crystal slabs1957.3.1Geometry of a photonic-crystal slab1957.3.2Eigenmodes of a photonic-crystal slab1977.3.3Analogy between the modes of a photonic-crystal slab and themodes of a corresponding2D photonic crystal2007.3.4Modes of a photonic-crystal slab waveguide2047.4Problems207References208 8Nonlinear effects and gap–soliton formation in periodic media2108.1Solitons bifurcated from Bloch bands in1D periodic media2118.1.1Bloch bands and bandgaps2118.1.2Envelope equations of Bloch modes2128.1.3Locations of envelope solitons2158.1.4Soliton families bifurcated from band edges2168.2Solitons bifurcated from Bloch bands in2D periodic media2188.2.1T wo-dimensional Bloch bands and bandgaps of linearperiodic systems2198.2.2Envelope equations of2D Bloch modes2208.2.3Families of solitons bifurcated from2D band edges2238.3Soliton families not bifurcated from Bloch bands2268.4Problems227References228Problem solutions230Chapter2230Chapter3236Chapter5244Chapter6246Chapter7257Chapter8260 Index263More informationPrefaceThefield of photonic crystals(aka periodic photonic structures)is experiencing anunprecedented growth due to the dramatic ways in which such structures can control,modify,and harvest theflow of light.The idea of writing this book came to M.Skorobogatiy when he was developingan introductory course on photonic crystals at the Ecole Polytechnique de Montr´e al/University of Montr´e al.Thefield of photonic crystals,being heavily dependent onnumerical simulations,is somewhat challenging to introduce without sacrificing thequalitative understanding of the underlying physics.On the other hand,exactly solvablemodels,where the relation between physics and quantitative results is most transpar-ent,only exist for photonic crystals of trivial geometries.The challenge,therefore,wasto develop a presentational approach that would maximally use intuitive analytical andsemi-analytical models,while applying them to complex and practically relevant pho-tonic crystal structures.We would like to note that the main purpose of this book is not to present the latestadvancements in thefield of photonic crystals,but rather to give a systematic,logical,andpedagogical introduction to this vibrantfield.The text is largely aimed at students andresearchers who want to acquire a rigorous,while intuitive,mathematical introductioninto the subject of guided modes in photonic crystals and photonic crystal waveguides.The text,therefore,favors analysis of analytically or semi-analytically solvable problemsover pure numerical modeling.We believe that this is a more didactical approach whentrying to introduce a novice into a newfield.To further stimulate understanding of thebook content,we suggest many exercise problems of physical relevance that can besolved analytically.In the course of the book we extensively use the analogy between the Hamiltonian for-mulation of Maxwell’s equations and the Hamiltonian formulation of quantum mechan-ics.We present both frequency and propagation-constant based Hamiltonian formula-tions of Maxwell’s equations.The latter is particularly useful for analyzing photoniccrystal-based linear and nonlinear waveguides andfibers.This approach allows us touse a well-developed machinery of quantum mechanical semi-analytical methods,suchas perturbation theory,asymptotic analysis,and group theory,to investigate many ofthe limiting properties of photonic crystals,which are otherwise difficult to investigatebased only on numerical simulations.M.Skorobogatiy has contributed Chapters2,3,4,5,and6of this book,and J.Y anghas contributed Chapter8.Chapters1and7were co-authored by both authors.More informationAcknowledgementsM.Skorobogatiy would like to thank his graduate and postgraduate program mentors,Professor J.D.Joannopoulos and Professor Y.Fink from MIT,for introducing him intothefield of photonic crystals.He is grateful to Professor M.Koshiba and ProfessorK.Saitoh for hosting him at Hokkaido University in2005and for having many excitingdiscussions in the area of photonic crystalfibers.M.Skorobogatiy acknowledges theCanada Research Chair program for making this book possible by reducing his teachingload.J.Y ang thanks the funding support of the US Air Force Office of Scientific Research,which made many results of this book possible.He also thanks the Zhou Pei-Yuan Centerfor Applied Mathematics at Tsinghua University(China)for hospitality during his visit,where portions of this book were written.Both authors are grateful to their graduate andpostgraduate students for their comments and help,while this book was in preparation.Especially,J.Y ang likes to thank Dr.Jiandong Wang,whose help was essential for hisbook writing.。

如何查PACC代码？PACC代码是《Physics Abstracts,Classification and Contents》的缩略。

PACC专业代码是英国科学文摘（INSPEC）用于论文分类的代码。

按照论文的内容将其分为十大类有0000，1000，……5000，……9000表示，例如：凝聚物质由6000及7000表示，其中6000内包括凝聚物质的结构、热学和力学性质，而7000内包括凝聚物质的电子结构、电学、磁学和光学性质。

再仔细分则由6100……6200等表示，例如6100表示液体和固体结构。

而X射线晶体结构测定及精确化技术表示固体结构的测定包含在6100中，而用6110M来表示。

所以要查出某一论文的PACC专业代码，应先确定该论文主要内容属于哪一大类，就在那一大类中找出其代码，其次再找出该论文包括的其它次要内容的代码。

国际物理学分类表PACC（Physics Abstracts, Classification andContents）0000 总论 GENERAL0100 通讯、教育、历史和哲学 communication,education,history,andphilosophy0110 通报、消息和组织活动announcements, news, and organizational activities0110C 通报、消息和颁奖announcements, news, and awards 0110F 会议、演讲和学会conferences, lectures, and institutes 0110H 物理学组织活动physics organizational activities 0130 物理学文献及出版物physics literature and publications0130B 讲稿的出版(进修学院,暑期学校等)publications of lectures (advanced institutes, summer schools, etc.)0130C 会议录 conferenceproceedings 0130E 专著和著作集 monographs,andcollections 0130K 手册和字典handbooks and dictionaries0130L 物理数据、表格汇编collections of physical data, tables0130N 教科书 textbooks0130Q 报告、学位论文、论文reports, dissertations, theses0130R 评论及教学参考论文,资源通讯reviews and tutorial papers, resource letters0130T 书目 bibliographies 0140 教育 education0140D 课程设置与评价course design and evaluation0140E 中小学科学science in elementary and secondary school0140G 课程设置,教学方法,策略和评价curricula, teaching methods, strategies, and evaluation0140J 教师培训 teachertraining0150 教具(包括设备和实验及教学用材料)educational aids(inc.equipment, experiments andteaching approaches to subjects)0150F 视听教具、电影audio and visual aids, films0150H 计算机在教学中的使用instructional computer use0150K 试验理论和技术testing theory and techniques0150M 示范教学的实验和设备demonstration experiments and apparatus 0150P 实验室实验和设备laboratory experiments and apparatus0150Q 实验室课程设置、组织和评价laboratory course design, organization, and evaluation0150T 建筑物和设备 buildingsandfacilities 0155 普通物理 generalphysics 0160 传记、历史和个人笔记biographical, historical, and personal notes 0165 科学史history of science0170 科学哲学 philosophyofscience 0175 科学与社会 scienceandsociety 0190 其他一般论题other topics of general interest0200 物理学中的数学方法mathematical methods in physics0210 代数、集合论和图论algebra, set theory, and graph theory0220 群论(量子力学中的代数方法见0365;基本粒子物理学中的对称见1130)group theory(for algebraic methods in quantummechanics, see 0365; for symmetries inelementary particle physics, see 1130)0230 函数论,分析function theory, analysis0240 几何学、微分几何学和拓扑学(0400相对论与引力)geometry, differential geometry, andtopology(0400 relativity and gravitation)0250 概率论、随机过程和统计学(0500统计物理学)probability theory, stochastic processes, andstatistics(0500 statistical physics)0260 数字近似及分析numerical approximation and analysis0270 计算技术(数据处理与计算见0650)computational techniques(for data handling and computation, see 0650)0290 物理学中数学方法的其它论题other topics in mathematical methods in physics0300 经典及量子物理学;力学与场classical and quantum physics; mechanics and fields0320 离散系统的经典力学:一般数学问题(离散系统的应用经典力学见4610;天体力学见9510)classical mechanics of discrete systems: generalmathematical aspects ( for applied classicalmechanics of discrete systems, see 4610; forcelestial mechanics, see 9510)0330 狭义相对论 specialrelativity0340 连续介质经典力学:一般数学问题classical mechanics of continuous media: general mathematical aspects0340D 弹性力学的数学理论(4620连续介质力学,4630固体力学)mathematical theory of elasticity(4620 continuummechanics, and 4630 mechanics of solids)0340G 流体动力学:一般数学问题(4700流体动力学)fluid dynamics; general mathematicalaspects(4700 fluid dynamics)0340K 波和波传播:一般数学问题(4630M机械波和弹性波;4320一般线性声学)waves and wave propagation; generalmathematical aspects(4630M mechanical andelastic waves, 4320 general linear acoustics)0350 经典场论 classicalfieldtheory0350D 麦克斯韦理论:一般数学问题(应用经典电动力学,见4100)Maxwell theory: general mathematical aspects(forapplied classical electrodynamics, see 4100)0350K 其它具体经典场论other special classical field theories0365 量子论;量子力学(0530量子统计力学;相对论性波动方程,见1110)quantum theory; quantum mechanics(0530quantum statistical mechanics;for relativisticwave equations, see 1110)0365B 基础、测量理论、其它理论foundations, theory of measurement, miscellaneous theories0365C 形式论 formalism 0365D 泛函分析方法functional analytical methods0365F 代数方法(0220群论;3115分子物理学中计算方法)algebraic methods(02 20 group theory; 3115calculation methods in molecular physics)0365G 波动方程解:边界态solutions of wave equations: bound state0365N 非相对论性散射理论 nonrelativisticscatteringtheory 0365S 半经典理论和应用semiclassical theories and applications0367 量子信息 Quantuminformation 0370 量子场论(1110场论) theory of quantized fields(1110 field theory)0380 散射的一般理论(1120 S-矩阵论;1180相对论性散射)general theory of scattering(1120 S-matrix theory,and 1180 relativistic scattering)0400 相对论与引力(狭义相对论,见0330;相对论性天体物理学,见9530; 相对论性宇宙学,见9880)relativity and gravitation(for special relarivity,see0330;for relativistic astrophysics,see 9530;forrelativistic cosmology,see 9880)0420 广义相对论(0240几何学和拓扑学)general relativity (0240 geometry and topology) 0420C 基本问题和普通形式论fundamental problems and general formalism0420F 典型的形式论、拉氏函数和变分原理canonical formalism, Lagrangians, and variationalprinciples0420J 方程解solutions to equations0420M 守恒定律和运动方程conservation laws and equations of motion 0430 引力波和辐射:理论gravitational waves and radiation: theory0440 连续介质;电磁及其它混合引力系统continuous media; electromagnetic and othermixed gravitational systems0450 统一场论及其它引力理论unified field theories and other theories of gravitation0455 引力替代理论alternative theories of gravitation0460 引力的量子论quantum theory of gravitation0465 超引力 supergravity0470 黑洞物理学(参见9760L 黑洞) physics of black holes (see also 9760L black holes)0480 广义相对论的实验检验及引力辐射观测experimental tests of general relativity andobservations of gravitational radiation0485 中程力(包括第五和第六力) intermediate range forces (inc.fifth and sixth forces)0490 相对论和引力的其它论题other topics in relativity and gravitation0500 统计物理学和热力学(0250概率论、随机过程和统计学)statistical physics and thermodynamics(0250probability thory,stochastic processes,andstatistics)0520 统计力学 statisticalmechanics 0520D 分子运动论 kinetictheory0520G 经典系综论classical ensemble theory0530 量子统计力学(6700量子流体;7100凝聚物质的电子态)quantum statistic al mechanics(6700 quantumfluids, and 7100 electron states in condensedmatter)0530C 量子系综论quantum ensemble theory0530F 费米子系统和电子气Fermion systems and electron gas 0530J 玻色子系统 Bosonsystems0530L 任意子和仲统计学(量子统计力学)anyons and parastatistics (quantum statistical mechanics)0540 涨落现象、随机过程和布朗运动fluctuation phenomena, random processes, and Brownian motion0545 混沌系统的理论和模型(流体系统中的混沌，见4752)theory and models of chaotic systems(for chaos inflowing systems,see 4752)0547 非线性动力学系统和分岔(流体系统中的分岔，见4752)nonlinear dynamical systems and bifurcations(bifurcations in flowing systems,see 4752)0550 点阵理论和统计学;伊辛问题(7510H伊辛模型)lattice theory and statistics; Ising problems(7510HIsing models)0555 分形(流体系统中的分形，见4752)fractals (fractals in flowing systems,see 4752) 0560 输运过程:理论 transportprocesses:theory 0565 自组织系统 Self-organizedsystems0570 热力学(4460热力学过程;6400状态方程,相平衡和相变;6500凝聚物质的热性质 ; 化学热力学,见8260)thermodynamics(4460 thermodynamic processes;6400 equation s of state, phase equilibria andphase transitions; 6500 thermal properties ofcondensed matter;for chemical thermodynamics,see 8260)0570C 热力学函数及状态方程thermodynamic functions and equations of state0570F 相变:一般问题phase transitions: general aspects 0570J 临界点现象critical point phenomena0570L 非平衡热力学、不可逆过程(3430势能表面;8200物理化学)nonequilibrium thermodynamics, irreversibleprocesses(3430 potential energy surfaces, 8200physical chemistry)0580 经济物理学 Econophysics0590 统计物理学和热力学的其它论题other topics in statistical physics and thermodynamics0600 测量科学、普通实验室技术及测试设备系统Measurement science, general laboratorytechniques, and instrumentation systems0620 基本度量学 metrology 0620D 测量与误差理论measurement and error theory0620F 单位 units 0620H 测量标准和校正measurement standards and calibration 0620J 基本常数测定determination of fundamental constants 0630 基本变量测量measurement of basic variables0630C 空间变量测量(包括空间延伸的所有变量如:直径、重量、厚度、位移、表面拓扑学、粒子尺寸、弥散系统区)spatial variables measurement(inc.measurementof all variables extending in space e.g. diameter,weight, thickness, displacement , surfacetopography, particle size, area of dispersesystems)0630E 质量与密度的测量mass and density measurement0630F 时间与频率的测量(天文学方面的,见9570)time and frequency measurement(for astronomicalaspects see 9570)0630G 速度、加速度和转动测量(流速测量,见4780)velocity, acceleration and rotationmeasurement(for flow velocity measurement see4780)0630L 基本电磁变量测量(0750电学仪器和技术)measurement of basic electromagneticvariables(0750 electrical instruments andtechniques)0630M 机械变量测量(包括弹性模量，力，冲击，应变，应力，力矩和振动)(压力测量，见0630N；声学变量测量，见4385D；固体力学测量，见4630R；粘度测量，见4780；材料试验，8170)measurement of mechanical variables(inc.elasticmoduli,force,shock ,strain,stress,torque,andvibration)(for pressure measurement,see0630N;for acoustic variables measurement,see4385D;for measurement in the mechanics ofsolids, see 4630R;for viscosity measurement,see4780;for materials testing,see 8170)0630N 压力测量(真空测量，见0730D；高压技术，见0735)pressure measurement(for vacuum measurement,see 0730D;for high-pressure techniques, see0735)0650 数据处理和计算(0270计算技术;2980核信息处理;光学数据处理,存贮及检索, 见423 0;地球物理数据采集和存贮,见9365)data handling and computation(0270computational techniques; 2980 nuclearinformation processing;for optical dataprocessing , storage and retrieval see 4230; forgeophysical data acquisition and storage see9365)0650D 数据搜集、处理、记录、数据显示(含数显技术)data gathering, processing, and recording, datadisplays (including digital techniques)0650M 计算装置与技术computing devices and techniques0660 实验室技术 laboratorytechniques 0660E 样品制备 samplepreparation0660J 高速技术(微秒到微微秒) high　speed techniques (microsecond to picosecond)0660S 微检验装置、微定位器和切片机micromanipulators, micropositioners , and microtomes0660V 车间技术(焊接、机械加工、润滑作用和轴承等)workshop techniques ( welding, machining,lubrication, bearings, etc.)0660W 安全(2880辐射监测和防护;8760M辐射剂量测定法;8760P辐射防护)safety( 2880 radiation monitoring and protection,8760M radiation dosimetry, 8760P radiationprotection)0670 普通测试设备 generalinstrumentation 0670D 敏感元件和探测器sensing and detecting devices0670E 试验设备 testingequipment 0670H 显示、记录与指示器display, recording, and indicating instrument s0670M 换能器(电磁辐射换能器见0762;声换能器见4388;液流换能器见4780)transducers(for electromagnetic radiationtransducers see 0762; for acoustic transducers see4388; for flow transducers see 4780)0670T 伺服及控制装置servo and control devices0690 测量科学、普通实验室技术及测试设备系统中的其它论题other topics in measurement science, generallaboratory techniques and instrumentationsystems0700 物理学中普遍使用的专用测试设备与技术(各分支学科的专用测试设备与技术入各自的分支学科)specific instrumentation and techniques of generaluse in physics(within each subdiscipline forspecialized instrumentation and techniques)0710 机械仪器与测量方法(固体力学测量见4630R;材料试验见8170)mechanical instruments and measurementmethods(for measurement in the mechanics of solids, see 4630R; for materials testing, see 8170)0710C 微机械器件和系统(微光学器件和技术，见4283)micromechanical devices and systems (formicrooptical devices and technology,see 4283)0710F 隔振 vibrationisolation0710Y 其他机械仪器和技术(包括摆、陀螺仪、离心器)other mechanical instruments andtechniques(inc.pendulums,gyroscopes,centrifuges)0720 热仪器和技术(4450物质的热性质;4460热力学过程;热辐射的辐射度学和检测, 见 0760D和0762)thermal instruments and techniques(4450 thermalproperties of matter, 4460 thermodynamicprocesses;for radiometry and detection of thermalradiation see 0760D and 0762)0720D 温度测量 thermometry 0720F 量热学 calorimetry 0720H 加热炉 furnaces0720K 高温技术及测试设备;测高温术high　temperature techniques and instrumentation; pyrometry0720M 低温实验法 cryogenics 0725 测湿法 hygrometry0730 真空产生与真空技术(包括低于1个大气压的压力;稀薄气体动力学入4745;8115 G 真空淀积)vacuum production and techniques(inc.pressuresbelow 1atmosphere; 4745 rarefied gas dynamics;8115G vacuum deposition)0730B 排空能力、除气、剩余气体evacuating power, degasification, residual gas 0730C 真空泵 vacuumpumps 0730D 真空计 vacuummeters 0730G 真空设备及试验方法vacuum apparatus and testing methods0730K 辅助设备、器件及材料auxiliary apparatus, hardware and materials0735 高压产生与技术(包括大于1个大气压的压力)high pressure production and techniques(inc.pressures above 1 atmosphere)0750 电学仪器及技术electrical instruments and techniques 0755 磁测量仪器及技术magnetic instruments and techniques0758 磁共振谱仪、辅助仪器和技术(6116N电子顺磁共振和核磁共振测定)magnetic resonance spectrometers, auxiliaryinstruments and techniques(6116N EPR and NMRdeterminations)0760 光学仪器和技术(辐射探测见0762;光谱学和光谱计见0765;全息术见4240;光源和标准见4272;光学透镜和反射系统见4278;光学器件、技术和应用见4280;光学试验和加工技术见4285;辐射谱仪和光谱技术见2930;辐射测量、检测和计数见2970)optical instruments and techniques(for radiationdetection, see 0762; for spectroscopy andspectrometers, see 0765; for holography, see4240; for optical sources and standards, see 4272;for optical lens and mirror systems, see 4278; foroptical devices , techniques and applications, see4280; for optical testing and workshop techniques,see 4285; for radiation spectrometers andspectroscopic techniques, see 29 30; for radiationmeasurement, detection and counting, see 2970)0760D 光度学和辐射度学(包括色度学,辐射探测入0762)photometry and radio metry(inc.colorimetry;0762detection of radiation)0760F 偏振测量术与椭园偏振测量术 polarimetryandellipsometry0760H 折射测量术与反射测量术 refractometryandreflectometry 0760L 干涉量度学 interferometry 0760P 光学显微术 opticalmicroscopy0762 辐射探测(测辐射热计、光电管、红外波与亚毫米波探测)detection of radiation (bolometers, photoelectriccells, IR. and submillimetre waves detection)0765 光谱学与光谱计(包括光声谱术) optical spectroscopy and spectrometers(inc.photoacoustic spectroscopy)0765E 紫外和可见光谱学与光谱仪UV and visible spectroscopy and spectrometers 0765G 红外光谱学与光谱仪IR spectroscopy and spectrometers0768 照相术、照相仪器与技术(光敏材料参见4270;照相过程的化学参见8250)photography, photographic instruments andtechniques(for light sensitive materials see also4270 for chemistry of photographic process seealso 8250)0775 质谱仪与质谱测定技术(质谱化学分析见8280)mass spectrometers and m ass spectrometrytechniques(for mass spectroscopic chemicalanalysis, see 8280)0777 粒子束的产生与处理;(2925基本粒子和核物理中的粒子源和靶;4180粒子束和粒子光学)particle beam production and handling;(2925particle sources and targets in elementary　particle and nuclear physics, 4180 particle beamsand particle optics)0779 扫描探针显微术及其相关技术(包括扫描隧道显微术，原子力显微术、磁力显微术，摩擦力显微术，和近场扫描光学显微术，(结构测定方面，参见6116P)scanning prob e microscopy and relatedtechniques(inc.scanning tunnellingmicroscopy,atomic force microscopy,magneticforce microscopy,friction force microscopy,andnear　field scanning opticalmicroscopy)(structure determination aspects, seealso 6116P)0780 电子与离子显微镜及其技术(6116D凝聚物质中的电子显微术;6116F凝聚物质中的场离子显微术)electron and ion microscopes andtechniques(6116D in condensed matter electronmicroscopy, 6116F field ion microscopy)0781 电子和离子谱仪及其相关技术(参见2930辐射谱仪和光谱技术)electron and ion spectrometers and relatedtechniques(see also 2930 radiation spectrometersan d spectroscopic techniques)0785 X射线与γ射线仪器与技术(包括穆斯堡尔谱仪和技术)X-ray, gamma-ray instruments and techniques(inc.Moessbauer spectrometers and technique s)0788 粒子干涉量度学和中子仪器(粒子束的产生与处理，参见0777;中子谱仪，参见 2930H ，原子干涉量度学，参见3580粒子光学，参见4180)particle interferometry and neutroninstrumentation(for particle beam production andhandling,see 0777;for neutron spectrometers,seealso 2930H;for atomic interferometry,see also3580;for particle optics,see also 4180)0790 专用设备中的其它论题other topics in specialised instrumentation1000 基本粒子物理与场(宇宙线见9440;高能实验技术和设备见 2900)THE PHYSICS OF ELEMENTARY PARTICLESAND FIELDS(for cosmic rays ,see 9440;for highenergy experimental techniques andinstrumentation, see 2900)1100 场和粒子的一般理论(0365量子力学;0370量子场论;0380散射的一般理论)general theory of fields and particles(0365quantum mechanics, 0370 theory of quantizedfields, 0380 general theory of scattering)1110 场论 fieldtheory 1110C 公理法 axiomaticapproach 1110E 拉氏函数和哈密顿函数法Lagrangian and Hamiltonian approach1110G 重正化 renormalization 1110J 渐近问题与特性asymptotic problems and properties1110L 非线性或非局域理论及模型nonlinear or nonlocal theories and models1110M 史文格源理论 Schwingersourcetheory 1110N 规范场论gauge field theories1110Q 相对论性波动方程relativistic wave equations1110S 束缚与非稳定态;贝特-沙耳皮特方程bound and unstable states; Bethe-Salpeterequations1110W 有限温度场论finite temperature field theory1117 弦理论和其他扩展物质理论(包括超弦和膜)theories of strings and other extendedobjects(inc.superstrings and membranes)1120 S-矩阵论 S-matrixtheory 1120D 散射矩阵和微扰论scattering matrix and perturbation theory1120F 色散关系和S矩阵的分析特性dispersion relations and analytic properties of the S-matrix1130 对称和守恒定律(0220群论) symmetry and conservation laws(0220 group theory)1130C 洛伦兹与庞加莱不变性Lorentz and Poincare invariance1130E 电荷共轭、宇称、时间反演和其它分立对称charge conjugation, parity, time reversal and otherdiscrete symmetries1130J SU(2)和SU(3)对称SU(2) and SU(3) symmetries1130K SU(4)对称 SU(4)symmetry 1130L 其他内部对称和高度对称other internal and higher symmetries1130N 非线性对称和动力学对称性(谱生成对称)nonlinear and dynamical symmetries (spectrum　generating symmetries)1130P 超对称 supersymmetry1130Q 自发性对称破缺spontaneous symmetry breaking1130R 手征对称 chiralsymmetries 1140 流及其特性currents and their properties1140D 流的一般理论general theory of currents1140F 流代数的拉格朗日算法Lagrangian approach to current algebras1140H 部分守恒轴矢量流partially conserved axial　vector currents 1150 色散关系与求和定则dispersion relations and sum rules1150E n/d法 n/dmethod 1150G 靴襻 bootstraps 1150J 交叉对称 crossingsymmetries 1150L 求和定则 sumrules1150N 多变量色散关系(包括曼德尔斯坦表象)multivariable dispersion relations(inc.Mandelstamrepresentation)1160 复合角动量;雷其(理论)体系(0380一般散射理论;1240强相互作用中的复合角动量)complex angular momentum; Reggeformalism(0380 general theory of scattering, 1240in strong interactions)1180 相对论性散射理论(0380一般散射理论)relativistic scattering theory (0380 general theoryof scattering)1180C 运动特性(螺旋性和不变振幅、运动奇异性等)kinematical properties (helicity and invariantamplitudes, kinematic singularities, etc.)1180E 部分波分析 partial　wave analysis1180F 近似法(程函近似法,变分原理等) approximations (eikonal approximation, variational principles, etc)1180G 多道散射 multichannelscattering 1180J 多体散射和Faddeev方程Many-body scattering and Faddeev equation 1180L 多次散射 multiplescattering 1190 一般场论和粒子理论的其它论题other topics in general field and particle theory1200 具体理论和相互作用模型;粒子分类系统specific theories and interaction models; particlesystematics1210 统一场论和模型unified field theories and models1210B 电弱理论 electroweaktheories 1210C 统一化标准模型standard model of unification1210D 标准模型以外的统一模型(包括GUTS，颜色模型和SUSY模型)unified models beyond the standardmodel(inc.GUTS,technicolour and SUSY models)1220 电磁相互作用模型models of electromagnetic interactions1220D 量子电动力学的具体计算和极限specific calculations and limits of quantum electrodynamics1220F 量子电动力学的实验检验experimental tests of quantum electrodynamics 1225 引力相互作用模型(0460引力的量models for gravitational interactions(0460子论) quantum theory of gravitation)1230 弱相互作用模型models of weak interactions1230C 中子流 neutralcurrents 1230E 中间玻色子 intermediatebosons 1235 粒子的复合模型composite models of particles1235C 量子色动力学的一般特性(动力学,禁闭等)general properties of quantum chromodynamics(dynamics, confinement, etc.)1235E 量子色动力学在粒子特性和反应中的应用applications of quantum chromodynamics toparticle properties and reactions1235H 粒子的结构和反应的唯象复合模型(部分子模型,口袋模型等)phenomenological composite models of particlestructure and reactions (partons, bags, etc.)1235K 其它复合模型(包括复合夸克模型和轻子模型)other composite models( posite quarksand leptons)1240 强相互作用模型models of strong interactions1240E 统计模型 statisticalmodels1240F 靴襻模型 bootstrapmodels1240H 二重性和双关模型duality and dual models1240K 强子分类方案 hadronclassificationschemes1240M 复合角动量平面;雷其极点和割线(雷其子)(1160复合角动量,雷其体系的一般理论)complex angular momentum plane; Regge polesand cuts (Reggeons)(1160 for general theory)1240P 吸收模型,光学模型和程函模型(衍射和衍射生成模型见1240S)absorptive, optical, and eikonal models(fordiffraction and diffractive production models, see1240S)1240Q 势模型 potentialmodels1240R 边缘碰撞模型(一个或多个粒子交换) peripheral models (one or more particle exchange)1240S 多重边缘碰撞模型和多雷其模型(包括衍射和衍射生成模型)multiperipheral and multi　Reggemodels(inc.diffraction and diffractive productionmodels)1240V 矢量介子优势 Vector-mesondominance 1270 强子质量公式hadron mass formulas1290 其它各种理论设想与模型miscellaneous theoretical ideas and models1300 具体基本粒子反应和唯象论specific elementary particle reactions and phenomenology1310 轻子间的弱相互作用和电磁相互作用weak and electromagnetic interactions of leptons1315 中微子相互作用(包括宇宙射线相互作用)neutrino interactions(inc.interactions involvingcosmic rays)1320 介子的轻子与半轻子衰变leptonic and semileptonic decays of mesons1320C π衰变 pidecays1320E K衰变 Kdecays1320G Ψ/J介子、Υ介子、Φ介子psi/J, upsilon, phi mesons1320H B介子轻子/半轻子衰变 Bmesonleptonic/semileptonicdecays 1320I f介子轻子/半轻子衰变 fmesonleptonic/semileptonicdecays 1320J 其它介子衰变other meson decays1325 介子的强子衰变 hadronicdecaysofmesons 1330 重子的衰变 decaysofbaryons1330C 轻子与半轻子衰变leptonic and semileptonic decays1330E 强子衰变 hadronicdecays 1335 轻子的衰变 decaysofleptons1338 中间玻色子和希格斯玻色子的衰变decays of intermediate and Higgs Bosons1340 电磁过程与特性electromagnetic processes and properties1340D 电磁质量差electromagnetic mass differences1340F 电磁形状因子、电矩和磁矩electromagnetic form factors; electric and magnetic moments1340H 电磁衰变 electromagneticdecays1340K 强相互作用和弱相互作用过程的电磁修正electromagnetic corrections to strong and weakinteraction processes1360 光子及带电轻子与强子的相互作用(中微子相互作用见1315)photon and charged　lepton interactions withhadrons(for neutrino interactions, see 1315)1360F 弹性散射与康普顿散射elastic and Compton scattering1360H 总截面和单举(反应)截面(包括深度非弹性过程)total and inclusive crosssections(inc.deep-inelastic processes)1360K 介子产生 mesonproduction 1360M 介子共振产生 Meson-resonanceproduction 1360P 重子和重子共振产生baryon and baryon resonance production1365 电子-正电子碰撞产生强子hadron production by electron-positron collisions1375 强子诱发的低能和中能反应及散射(能量≤10GeV见1385)Hadron-induced low　energy and intermediate　energy reactions and scattering, energy ≤10GeV( for higher energies, see 1385)1375C 核子-核子相互作用,包括反核子和氘核等(能量≤10GeV;核中的核子-核子相互作用见2130)Nucleon-nucleon interactions, includingantinucleon, deuteron, etc. (energy ≤10GeV)(for n-n interactions in nuclei, see 2130)1375E 超子-核子相互作用(能量≤10GeV)Hyperon-nucleon interactions (energy ≤10 GeV)1375G π介子-重子相互作用(能量≤10GeV) Pion-baryon interactions (energy ≤10 GeV)1375J K介子-重子相互作用(能量≤10GeV) Kaon-baryon interactions (energy ≤10 GeV)1375L 介子-介子相互作用(能量≤10GeV)Meson-meson interactions (energy ≤10 GeV) 1380 光子-光子相互作用和散射 Photon-photon interactions and scattering1385 强子诱发的高能和超高能相互作用(能量>10GeV)(低能情况见1375) Hadron-induced high-energy and super-high-energy interactions, energy > 10GeV(for low energies, see 1375)1385D 弹性散射(能量=10GeV) elastic scattering (energy = 10 GeV)1385F非弹性散射、双粒子终态(能量>10GeV) inelastic scattering, two-particle final states(energy > 10 GeV) 1385H 非弹性散射、多粒子终态(能量>10GeV) inelastic scattering, many-particle final states(energy>10GeV)1385K 单举反应,包括总截面(能量>10GeV) inclusive reactions, including total cross sections,(energy > 10 GeV)1385M 宇宙射线相互作用(9440宇宙线) cosmic ray interactions(9440 cosmic rays)1385N 强子诱发的高能相互作用(能量>1TeV) hadron induced very high energy interactions(energy>1 TeV)1387大Q2基本粒子相互作用中的射流jets in large-Q2 elementary particle interactions 1388相互作用和散射中的极化 polarisation in interactions and scattering 1390基本粒子的具体反应及唯象论的其它论题 other topics in specific reactions and phenomenology of elementary particles 1400具体粒子的性质与共振 properties of specific particles and resonances 1420 重子与重子共振(包括反粒子) baryons and baryon resonances(inc.antiparticles)1420C 中子 neutrons1420E 质子 protons1420G s =0时的重子共振baryon resonances with s=0 1420J超子和超子共振 hyperons and hyperon resonances 1420P双重子 dibaryons1440 介子和介子共振 mesons and meson resonances 1440D π介子 pi mesons1440F K 介子 K mesons1440K Ρ介子、Ω介子和η介子rho, omega, and eta mesons 1440L d 介子和F 介子d and F mesons 1440N Ψ/J 介子、Υ介子、Φ介子psi/J, upsilon, phi mesons 1440P其它介子 other mesons 1460 轻子 leptons1460C 电子和正电子 electrons and positrons 1460E μ介子 muons1460G 中微子 neutrinos1460J重轻子 heavy leptons 1480 其它粒子和假设粒子 other and hypothetical particles1480A 光子 photons1480D 夸克和胶子 quarksandgluons 1480F 中间玻色子 intermediateBosons 1480H 磁单极子 magneticmonopoles1480J 超对称粒子(包括标量粒子，超粒子和超离子)Supersymmetric particles(inc.scalarparticles,superparticles and superions)1480K 其它(包括快子) others(inc.tachyons)2000 核物理学 NUCLEARPHYSICS 2100 核结构 nuclearstructure2110 核的一般和平均性质;核能级性质(按质量范围分类的具体核的性质见2700)general and average properties of nuclei;properties of nuclear energy levels(for propertiesof specific nuclei listed by mass ranges, see 2700)2110D 结合能和质量binding energy and masses2110F 形状、电荷、半径和形状因子shape, charge, radius and form factor s2110H 自旋、宇称和同位旋spin, parity, and isobaric spin2110J 谱因子 spectroscopicfactors 2110K 电磁矩 electromagneticmoments 2110M 能级密度和结构level density and structure2110P 单粒子能级结构single particle structure in levels2110R 集团能级结构(包括旋转能带) collective structure in levels(inc.rotational bands) 2110S 库仑效应 Coulombeffects2130 核力(1375C核子-核子相互作用) nuclear forces(1375C nucleon-nucleon interactions)2140 少核子系统 Few-nucleonsystems2160 核结构模型与方法(强子的原子和分子见3610)nuclear　structure models and methods(forhadronic atoms and molecules, see 3610)2160C 壳层模型 shellmodel2160E 集体模型 collectivemodels 2160F 群论模型models based on group theory2160G 集团模型 clustermodels 2160J 哈特里-福克和随机-相位近似Hartree-Fock and random-phase approximations 2165 核物质 nuclearmatter 2180 超核 hypernuclei 2190 核结构的其它论题other topics in nuclear structure2300 放射性和电磁跃迁(8255放射化学)radioactivity and electromagnetic transitions(8255 radiochemistry)2320 电磁跃迁 electromagnetictransitions 2320C 寿命和跃迁几率lifetimes and transition probabilities2320E 角分布和校正测量angular distribution and correlation measurements2320G 多极混合比率 multipolemixingratios 2320J 多极矩阵元素 multipolematrixelements 2320L γ跃迁和能级gamma transitions and level energies2320N 内转换和核外效应internal conversion and extranuclear effects 2320Q 核共振荧光nuclear resonance fluorescence2340 β衰变;电子与μ子俘获beta decay; electron and muon capture2340B 弱相互作用和β衰变的轻子特性weak interaction and lepton aspects of beta decay2340H 核矩阵元和从β衰变推断核结构nuclear matrix elements and nuclear structure inferred from beta decay2360 α衰变 alphadecay 2390 核衰变和放射性的其它论题other topics in nuclear decay and radioactivity 2400 核反应和散射:总论nuclear reactions and scattering:general2410 核反应和散射模型与方法nuclear reaction and scattering models and methods2410D 耦合道和多体论方法coupled　channel and many　body　theory methods2410F 平面和扭曲波玻恩近似法Plane- and distorted-wave Born approximations 2410H 光学模型和衍射模型optical and diffraction models2430 共振反应与散射resonance reactions and scattering2430C 巨共振 giantresonances 2430F 同位旋相似共振 isobaricanalogresonances 2450 直接反应 directreactions 2460 统计理论和涨落statistical theory and fluctuations2470 反应和散射中的极化polarization in reactions and scattering2475 裂变的一般性质general properties of fission2485 原子核和核形成过程的夸克模型quark models in nuclei and nuclear processes2490 核反应和散射的其它论题:一般问题other topics in nuclear reactions and scattering:general2500 核反应和散射:具体反应nuclear reactions and scattering:specific reactions2510 少核子系统的核反应与散射nuclear reactions and scattering involving few-nucleon systems2520 光致核反应和光子散射 photonuclearreactions and photon scattering 2530 轻子诱发反应与散射Lepton-induced reactions and scattering 2530C 电子和正电子反应与散射electron and positron reactions and scattering 2530E μ介子反应和散射muon reactions and scattering2530G 中微子反应和散射neutrino reactions and scattering。

为四季着色半命题英语作文600字叙事全文共3篇示例，供读者参考篇1Coloring the Four SeasonsWhen I was younger, the changing of the seasons always felt like a sort of magic to me. The greening of the trees in spring, the lush vibrance of summer, the crisp chill and brilliant colors of autumn, the sparkling pure white blanket of winter snow – it was like Mother Nature was an artist, repainting the landscape every few months with a fresh new palette of colors and textures. As I've grown older, the magic hasn't faded, but I've come to appreciate the cycles of the seasons on a deeper level.Spring's awakening is a time of renewal, rebirth, new beginnings. After being muted and dormant all winter, the Earth seems to stretch itself awake, slowly at first with patches of green poking through the thawing ground. Then almost overnight, it explodes into a frenzy of activity – buds appear on the trees, flowers bloom in kaleidoscopic abundance, birds busily construct nests and serenade with cheerful songs at dawn. The air smells fresh and earthy, full of postential. Spring is the season of hope.The initial euphoria of spring matures into the lush splendor of summer. The landscape is lush and green, trees in full leaf providing shady canopies. Gardens overflow with ripe vegetables and bright blooms. Soft breezes rustle through fields ofknee-high grass and wild flowers. The days are long and warm, the summer sun's rays turning exposed skin tan and freckled. This is the season of growth, activity, and adventuring outdoors. Balmy summer nights are made for campfires, grilling outdoors, catching fireflies in mason jars. Sipping lemonade on the porch as the heat of the day gives way to pleasant evenings. Summer's vibrancy is intoxicating.All too soon, summer's blaze of glory winds down to autumn's spectacular farewell. An artist could never quite capture the perfect medley of crimson, amber, ochre, and burnished gold that paints the woods when autumn takes hold. The air develops a clarity, a crisp coolness that rejuvenates the spirit. The summer's oppressive humidity breaks, replaced by pleasantly chilly nights ideal for cuddling up with a mug of hot cider in front of the fireplace. Autumn is a season of transition, transforming from one extreme of life to the other. The harvest is gathered, squirrels busily cache nuts, and migratory birds take flight for warmer destinations. The landscape puts on one last breathtaking show before shutting down for winter.When winter arrives, it sweeps the slate clean in pristine white. A fresh blanket of snow covers the ground, outlining every twig and branch in sparkling icy grandeur. The world seems to exist in stark, frozen beauty – black trees etched against snowy backdrops, animal tracks writing temporal stories in thenew-fallen powder. Life hasn't ceased, but just gone dormant –resting, waiting, slumbering through the coldest months until spring's reawakening. Winter's silent tranquility is beautifully serene, a peaceful respite after the frenetic energy of the other seasons. Time seems to slow, an inhale before the cycle begins anew.The seasons are a rhythm, each transitioning to the next in a perpetual dance as predictable as the passage of night to day. Yet there is an impermanence to them as well, a sense that this particular spring, this summer, autumn or winter will never come quite this way again. The seasons remind us to live fully in the present moment, to soak up and savor each one while we have it. For in their constant ebb and flow, we're reminded that all things must pass, and renewed again with a sense of appreciation for each tumbling turn of nature's kaleidoscope.篇2The Four Colored FrustrationIt was a crisp autumn morning, the kind where the air smelled of fresh beginnings and the leaves were just starting to turn brilliant shades of red and orange. I took a deep breath as I walked through the campus gates, savoring the mild chill and the dappled sunlight filtering through the old oak trees. A new school year stretched out before me, ripe with possibilities. Little did I know, one of those possibilities would nearly drive me mad by winter's end.It started innocently enough in my Discrete Mathematics class. Professor Robinson was known for being brilliant but...quirky. His lectures jumped rapidly from topic to topic, chasing the threads of his grand unified theory of mathematics like a dog chasing squirrels. On this particular day, he was discussing graph colorings and their applications to mapping, scheduling, and optimization problems."...And that's why the map coloring problem is so important," he said, his eyes bright behind his thick glasses. "Using the minimum number of colors to color a map such that no neighboring regions share the same color has widespread applications in efficient planning and resource allocation."I dutifully took notes, my pen scratching across the page. Graph theory made sense to me so far. Nodes, edges, colorings - it was like a big puzzle to solve.Then Professor Robinson's lecture took a dark turn. "Of course, the classic map coloring problem assumes an infinite number of available colors. But what happens when we constrain the number of colors? The four color theorem states that any map on a sphere can be colored using at most four colors such that no neighboring regions share the same color. Seems simple enough at first, doesn't it?"An uneasy feeling crept into my stomach. I could sense the other shoe about to drop."But what if we make it even harder?" Professor Robinson cackled, a mischievous glint in his eyes. "What if the colors have a...half-life?"A confused murmur rippled through the lecture hall. Half-life? Like radioactive materials? What did that have to do with map colorings?Professor Robinson clarified, "Imagine you have taken a beautifully colored map, using at most four colors, with no adjacent regions sharing the same color. So far, so good. Butthen the colors start to decay at an exponential rate, like radioactive particles. After one unit of time, any region colored red will change to an adjacent non-red color. After another unit of time, any remaining red regions will change to yet another color, and so on, cycling through the available colors."My mind struggled to picture this bizarre scenario. Colors...decaying and changing over time? On a map?"The half-life coloring problem," Professor Robinson continued, a crazed enthusiasm entering his voice, "Is to find a way to color the map using at most four colors such that no matter how the colors decay, no two neighboring regions will ever share the same color! It's a massively complex problem in computational complexity theory that remains unsolved to this day. Who wants to take a crack at it?"The lecture hall was deathly silent. A few students slowly raised their hands, more out of pity than actual understanding. Professor Robinson rubbed his hands together greedily."Excellent! Let's dive into theabyss..."And just like that, my life took an unsettlingly colorful turn down the rabbit hole of the half-life coloring problem. For the rest of that semester, it consumed my every waking thought. Ispent long nights in the library, scrambling between books on graph theory, combinatorics, and discrete mathematics, searching for a solution that always seemed just out of reach.The problem wiggled its way into my subconscious, haunting my dreams. I'd wake up in a cold sweat, the fractured hues of maps flickering behind my eyelids like demented Christmas lights. No matter how I arranged and rearranged the colors, the patterns always decayed into chaos.My friends stopped asking me to hang out, recognizing the vacant stare that meant I was mentally grappling with the facets of the problem yet again. I'm sure I came across as deeply unhinged, mumbling to myself about half-lives and color permutations. At my lowest points, I feared I would slip entirely into topological madness.Winter came and went in a blur of manic calculations and failed proofs. By the time spring's warm breezes and cherry blossoms arrived, I was a shell of my former self. Dark circles hung under my eyes, my skin was pale from spending too much time in the library archives, and I had grown an unkempt quarantine beard rivaling the infamous math genius Grigoriev Perelman.It all came to a head during my final exam for Discrete Mathematics. I stared numbly at the test booklet, the questions swimming before my eyes. My brain felt simultaneously overcrowded with half-baked ideas and terrifyingly empty. When I reached the final extra credit problem, the words seemed to leap off the page in a blaze of color:"Propose a solution to the four color half-life problem."In that moment, something inside me snapped like an overstressed mayorial. I let out a primal scream, shocking the entire exam hall into silence. Clutching the test booklet accusingly, I shouted, "You want a solution?! I'll give you a solution, you sadistic number goblins!"As a concerned professor rushed over, I proceeded to rant and rave about my many intricate but ultimately flawed approaches to the half-life coloring problem. I raved about the Exponential-Time conjecture, Manitoba nightshades,non-Abelian symmetries, and the fundamental impossibility of achieving a perfect steady-state of colors without risking the random heat-death of information. I may have even dabbled in number theoretic geometric mysticism and topological Kabbalah towards the end.Needless to say, I was gently but firmly escorted out of the exam hall by campus security. As I was dragged away, still raving like a lunatic about the cruel injustice of unsolvable combinatorics problems, I caught Professor Robinson's eye. The old madman gave me a wry smile and raised his coffee mug in a mock salute, as if to say "You fought a good fight against the half-life, my colorful friend."I ended up having to take an extended medical leave from school to recover from my descent into mathematical madness. To this day, I still get faraway looks in my eyes whenever I see a map or random splattering of colors. Sane people learn to avoid such topics around me.As for the four color half-life problem? It remains stubbornly unsolved, haunting the fringes of pure mathematics like a specter. I keep an eye on developments from a safe distance. Every few years, a brash young mathematician will arrogantly claim to have conquered the half-life beast, only to be brutally disproven and reduced to a gibbering, color-addled wreck like I was.The half-life colors may fade, but they never truly go away. They lurk in the shadowy recesses of Hilbert's cosmic infinite Hotel California, biding their time to entrap another generationof hapless problem solvers with their siren song of decaying chromatic chaos. The scarred survivors like me can only weakly raise our tattered graph theory texts and whisper a warning:"Abandon all colors, ye who venture here..."篇3Coloring the Seasons with Semi-LifeAs a student, the cycle of the seasons often feels like a never-ending carousel, spinning round and round with dizzying speed. The vibrant hues of autumn give way to the crisp whites and blues of winter, which melt into the gentle greens and pinks of spring, only to burst into the bold sunshine shades of summer before the cycle begins anew. Each season brings its own unique rhythms, challenges, and moments of semi-life to navigate.Autumn always arrives in a blaze of glory, the trees putting on one last fiery show before shedding their leaves. It's a time laden with fresh starts - new classes, new goals, reunions with friends. Yet it's also tinged with an underlying melancholy, the first hint of winter's chill in the air. The semi-life moments emerge in the quiet lulls between studying for midterms, when I find myself gazing wistfully out the window at the kaleidoscopeof reds, oranges, and yellows. It's a bittersweet pause, knowing this vibrant beauty is fleeting.Then, virtually overnight, winter descends. The world turns harsh and unforgiving, a stark monochrome punctuated only by the occasional deep evergreen. Suddenly, semi-life is a beloved mug of hot chocolate, clutched between numb hands as the wind howls relentlessly. It's the simple joy of watching fat snowflakes drift lazily earthwards from the lecture hall's frosty windows. Yet winter is also a slog, the dark mornings and early nights sapping motivation and energy. We dream of spring, even as we're huddled under layers battling the Arctic blasts.At long last, the thaw sets in and spring emerges like a shy debutante, timid but full of promise. The semi-life moments are countless - the first crocus bravely pushing through the crusty remains of snow, the delicate greening of the trees, the electrifying scent of rain-soaked earth. There's a buzzing vitality to spring that's utterly intoxicating after winter's slumber. My favorite semi-life instants are the ones I stumble upon unawares - rounding a corner to be enveloped in a cloud of pale pink blossoms, or spotting a kaleidoscope of butterflies dancing among the new blooms.Yet for all spring's delicate beauty, its ephemeral nature is a melancholy reminder that nothing lasts forever. Before we can fully acclimate, spring's hues deepen and blaze into summer's brash vibrancy. The semi-life beats of summer are loud, unapologetic, and tinged with the electric crackle of distant thunder. It's the hazy heat shimmering off the asphalt, water balloon fights on the quad, and the unmistakable aroma of sunscreen mingling with freshly-cut grass. Summer demands we live completely in the moment, chasing ice cream trucks, splashing in pools, and lying on our backs watching clouds morph into fantastical shapes.Too soon, the summer reaches its zenith and the cycle begins anew, autumn's brush stroking the canvas with those first few crimson harbingers. We blink and the semi-life rhythm modulates once more, trading the pulsating cacophony of summer for the wistful melancholy of fall. It's been another year spun round the carousel of life, each season leaving its vivid imprint.As a student, I've come to realize these simple semi-life moments are what make the cavalcade of semesters, papers, and exams bearable, even joyous. They're the splashes of color that transform the academic monochrome into a vibrant,ever-shifting masterpiece. Without them, the years would blur together into a lifeless grayscale. So I've learned to appreciate each one, no matter how small or fleeting, because therein lies the secret to not just surviving, but thriving, as the kaleidoscope of life keeps turning.。

a rXi v:h ep-ph/312335v123Dec23International Journal of Modern Physics A c World Scientific Publishing Company MIRROR WORLD AND ITS COSMOLOGICAL CONSEQUENCES ZURAB BEREZHIANI Dipartimento di Fisica,Universit`a di L’Aquila,67010Coppito,L’Aquila,and INFN,Laboratori Nazionali del Gran Sasso,67010Assergi,L’Aquila,Italy;e-mail:berezhiani@fe.infn.it We briefly review the concept of a parallel ‘mirror’world which has the same particle physics as the observable world and couples to the latter by gravity and perhaps other very weak forces.The nucleosynthesis bounds demand that the mirror world should have a smaller temperature than the ordinary one.By this reason its evolution should substan-tially deviate from the standard cosmology as far as the crucial epochs like baryogenesis,nucleosynthesis etc.are concerned.In particular,we show that in the context of certain baryogenesis scenarios,the baryon asymmetry in the mirror world should be larger than in the observable one.Moreover,we show that mirror baryons could naturally consti-tute the dominant dark matter component of the Universe,and discuss its cosmological implications.Keywords :Extensions of the standard model;baryogenesis;dark matter 1.Introduction The old idea that there can exist a hidden mirror sector of particles and interactions which is the exact duplicate of our visible world 1has attracted a significant interest over the last years.The basic concept is to have a theory given by the productG ×G ′of two identical gauge factors with the identical particle contents,which could naturally emerge e.g.in the context of E 8×E ′8superstring.In particular,one can consider a minimal symmetry G SM×G ′SM ,where G SM =SU (3)×SU (2)×U (1)stands for the standard model of observable particles:three families of quarks and leptons and the Higgs,while G ′SM =[SU (3)×SU (2)×U (1)]′is its mirror gauge counterpart with analogous particle content:three families of mirror quarks and leptons and the mirror Higgs.(From now on all fields and quantities of the mirror (M)sector will be marked by ′to distinguish from the ones belonging to the observable or ordinary (O)world.)The M-particles are singlets of G SM and vice versa,the O-particles are singlets of G ′SM .Besides the gravity,the two sectors could communicate by other means.In particular,ordinary photons could have kinetic mixing with mirror photons 2,3,4,ordinary (active)neutrinos could mix with mirror (sterile)neutrinos 5,6,or two sectors could have a common gauge symmetry of flavour 7.A discrete symmetry P (G ↔G ′)interchanging corresponding fields of G and G ′,so called mirror parity,guarantees that both particle sectors are described by12Zurab Berezhianithe same Lagrangians,with all coupling constants (gauge,Yukawa,Higgs)having the same pattern,and thus their microphysics is the same.If the mirror sector exists,then the Universe along with the ordinary photons,neutrinos,baryons,etc.should contain their mirror partners.One could naively think that due to mirror parity the ordinary and mirror particles should have the same cosmological abundances and hence the O-and M-sectors should have the same cosmological evolution.However,this would be in the immediate conflict with the Big Bang nucleosynthesis (BBN)bounds on the effective number of extra light neutrinos,since the mirror photons,electrons and neutrinos would give a contribu-tion to the Hubble expansion rate equivalent to ∆N ν≃6.14.Therefore,in the early Universe the M-system should have a lower temperature than ordinary particles.This situation is plausible if the following conditions are satisfied:A.After the Big Bang the two systems are born with different temperatures,namely the post-inflationary reheating temperature in the M-sector is lower than in the visible one,T ′R <T R .This can be naturally achieved in certain models 8,9,10.B.The two systems interact very weakly,so that they do not come into thermal equilibrium with each other after reheating.This condition is automatically fulfilled if the two worlds communicate only via gravity.If there are some other effective couplings between the O-and M-particles,they have to be properly suppressed.C.Both systems expand adiabatically,without significant entropy production.If the two sectors have different reheating temperatures,during the expansion of the Universe they evolve independently and their temperatures remain different at later stages,T ′<T ,then the presence of the M-sector would not affect primordial nucleosynthesis in the ordinary world.At present,the temperature of ordinary relic photons is T ≈2.75K,and the mass density of ordinary baryons constitutes about 5%of the critical density.Mirror photons should have smaller temperature T ′<T ,so their number density is n ′γ=x 3n γ,where x =T ′/T .This ratio is a key parameter in our further considerations since it remains nearly invariant during the expansion of the Universe.The BBN bound on ∆N νimplies the upper bound x <0.64∆N 1/4ν.As for mirror baryons,ad hoc their number density n ′b can be larger than n b ,and if the ratio β=n ′b /n b is about 5or so,they could constitute the dark matter of the Universe.In this paper we study the cosmology of the mirror sector and discuss the com-parative time history of the two sectors in the early Universe.We show that due to the temperature difference,in the mirror sector all key epochs as the baryoge-nesis,nucleosynthesis,etc.proceed at somewhat different conditions than in the observable Universe.In particular,we show that in certain baryogenesis scenarios the M-world gets a larger baryon asymmetry than the O-sector,and it is pretty plausible that β>1.11This situation emerges in a particularly appealing way in the leptogenesis scenario due to the lepton number leaking from the O-to the M-sector which leads to n ′b ≥n b ,and can thus explain the near coincidence of visible and dark components in a rather natural way 12,13.Mirror World (3)2.Mirror world and mirror symmetry2.1.Particles and couplings in the ordinary worldNowadays almost every particle physicist knows that particle physics is described by the Standard Model(SM)based on the gauge symmetry G SM=SU(3)×SU(2)×U(1),which has a chiral fermion pattern:fermions are represented as Weyl spinors, so that the left-handed(L)quarks and leptonsψL=q L,l L and right-handed(R) onesψR=q R,l R transform differently under the SU(2)×U(1)gauge factor.More precisely,the fermion content is the following:l L= νL e L ∼(1,2,−1);l R= N R∼(1,1,0)(?)e R∼(1,1,−2)q L= u L d L ∼(3,2,1/3);q R= u R∼(3,1,4/3)d R∼(3,1,−2/3),(1) where the brackets explicitly indicate the SU(3)and SU(2)content of the multiplets and their U(1)hypercharges.In addition,one prescribes a global lepton charge L=1to the leptons l L,l R and a baryon charge B=1/3to quarks q L,q R,so that baryons consisting of three quarks have B=1.The SU(2)×U(1)symmetry is spontaneously broken at the scale v=174GeV and W±,Z gauge bosons become massive.At the same time charged fermions get masses via the Yukawa couplings(i,j=1,2,3are the fermion generation indexes) L Yuk=Y u ij d R q Ljφd+Y e ij4Zurab BerezhianiHowever,one can simply redefine the notion of particles,namely,to callψL,˜ψL as L-particles and˜ψR,ψR,as R antiparticlesL−fermions:ψL,˜ψL;˜R−antifermions:˜ψR,ψR(5) Hence,the standard modelfields,including Higgses,can be recasted as:a L−set:(q,l,˜u,˜d,˜e,˜N)L,φu,φd;˜R−set:(˜q,˜l,u,d,e,N)R,˜φu,˜φd(6) where˜φu,d=φ∗u,d,and the the Yukawa Lagrangian(2)can be rewritten asL Yuk=˜u T Y u qφu+˜d T Y d qφd+˜e T Y e lφd+h.c.(7) where the C-matrix as well as the family indices are omitted for simplicity.In the absence of right-handed singlets N there are no renormalizable Yukawa couplings which could generate neutrino masses.However,once the higher order terms are allowed,the neutrinos could get Majorana masses via the D=5operators:A ij2(M ij N i N j+M∗ij˜N i˜N j).It is convenient to parametrize their mass matrix as M ij=G ij M,where M is a typical mass scale and G is a matrix of dimensionless Yukawa-like constants.On the other hand,the˜N states can couple to l via Yukawa terms analogous to(7), and thus the whole set of Yukawa terms obtain the pattern:l T Y˜Nφu+M10.In SO(10) model all L fermions in(5)sit in one representation L∼16,while the R anti-fermions sit in˜R∼Mirror World (5)symmetric with respect to exchange of the L particles to the R ones.In particular,the gauge bosons of SU(2)couple to theψLfields but do not couple toψR.Infact,in the limit of unbroken SU(2)×U(1)symmetry,ψL andψR are essentiallyindependent particles with different quantum numbers.The only reason why we calle.g.states e L⊂l L and e R respectively the left-and right-handed electrons,is that after the electroweak breaking down to U(1)em these two have the same electriccharges and form a massive Dirac fermionψe=e L+e R.Now what we call particles(1),the weak interactions are left-handed(V−A)since only the L-states couple to the SU(2)gauge bosons.In terms of antiparticles(3),the weak interactions would be right-handed(V+A),since now only R statescouple to the SU(2)bosons.Clearly,one could always redefine the notion of particlesand antiparticles,to rename particles as antiparticles and vice versa.Clearly,thenatural choice for what to call particles is given by the content of matter in ourUniverse.Matter,at least in our galaxy and its neighbourhoods,consists of baryonsq while antibaryons˜q can be met only in accelerators or perhaps in cosmic rays.However,if by chance we would live in the antibaryonic island of the Universe,wewould claim that our weak interactions are right-handed.In the context of the SM or its grand unified extensions,the only good symmetrybetween the left and right could be the CP symmetry between L-particles and R-antiparticles.E.g.,the Yukawa couplings(7)in explicit form readL=(˜u T Y u qφu+˜d T Y d qφd+˜e T Y e lφd)L+(u T Y∗u˜q˜φu+d T Y∗d˜q˜φd+e T Y∗e˜l˜φd)R(10) However,although these terms are written in an symmetric manner in terms of the L-particles and˜R-antiparticles,they are not invariant under L→˜R due to irremovable complex phases in the Yukawa coupling matrices.Hence,Nature does not respect the symmetry between particles and antiparticles,but rather applies the principle that”the only good discrete symmetry is a broken symmetry”.It is a philosophical question,who and how has prepared our Universe at theinitial state to provide an excess of baryons over antibaryons,and thereforefixed apriority of the V−A form of the weak interactions over the V+A one.It is appealingto think that the baryon asymmetry itself emerges due to the CP-violating featuresin the particle interactions,and it is related to some fundamental physics beyondthe Standard Model which is responsible for the primordial baryogenesis.2.2.Particles and couplings in the O-and M-worldsLet us assume now that there exists a mirror sector which has the same gauge groupand the same particle content as the ordinary one.In the minimal version,whenthe O-sector is described by the gauge symmetry G SM=SU(3)×SU(2)×U(1)with the observable fermions and Higgses(6),the M-sector would be given by thegauge group G′SM=SU(3)′×SU(2)′×U(1)′with the analogous particle content: L′−set:(q′,l′,˜u′,˜d′,˜e′,˜N′)L,φ′u,φ′d;˜R′−set:(˜q′,˜l′,u′,d′,e′,N′)R,˜φ′u,˜φ′d(11)6Zurab BerezhianiIn more general view,one can consider a supersymmetric theory with agauge symmetry G×G′based on grand unification groups as SU(5)×SU(5)′,SO(10)×SO(10)′,etc.The gauge factor G of the O-sector contains the vectorgauge superfields V,and left chiral matter(fermion and Higgs)superfields L a incertain representations of G,while G′stands for the M-sector with the gauge su-perfields V′,and left chiral matter superfields L′a∼r a in analogous representations of G′.The Lagrangian has a form L gauge+L mat.The matter Lagrangian is determinedby the form of the superpotential which is a holomorphic function of L superfieldsand in general it can contain any gauge invariant combination of the latter: W=(M ab L a L b+g abc L a L b L c)+(M′ab L′a L′b+g′abc L′a L′b L′c)+ (12)where dots stand for possible higher order ly,we haveL mat= dθ2W(L)+h.c.(13) or,in explicit form,L mat= dθ2(M ab L a L b+g abc L a L b L c+M′ab L′a L′b+g′abc L′a L′b L′c)+ dMirror World (7)Either type of parity implies that the two sectors have the same particle physics.c If the two sectors are separate and do not interact by forces other than gravity, the difference between D and P parities is rather symbolic and does not have any profound implications.However,in scenarios with some particle messengers between the two sectors this difference can be important and can have dynamical consequences.2.3.Couplings between O-and M-particlesNow we discuss,what common forces could exist between the O-and M-particles, including matterfields and gaugefields.•Kinetic mixing term between the O-and M-photons2,3,4.In the context of G SM×G′SM,the general Lagrangian can contain the gauge invariant termL=−χBµνB′µν,(19) where Bµν=∂µBν−∂νBµ,and analogously for B′µν,where Bµand B′µare gauge fields of the abelian gauge factors U(1)and U(1)′.Obviously,after the electroweak symmetry breaking,this term gives rise to a kinetic mixing term between thefield-strength tensors of the O-and M-photons:L=−εFµνF′µν(20) withε=ξcos2θW.There is no symmetry reason for suppressing this term,and generally the constantεcould be of order1.On the other hand,experimental limits on the orthopositronium annihilation imply a strong upper bound onε.This is because one has to diagonalizefirst the kinetic terms of the Aµand A′µstates and identify the physical photon as a certain linear combination of the latter.One has to notice that after the kinetic terms are brought to canonical form by diagonalization and scaling of thefields, (A,A′)→(A1,A2),any orthonormal combination of states A1and A2becomes good to describe the physical basis.In particular,A2can be chosen as a”sterile”state which does not couple to O-particles but only to M-particles.Then,the orthogonal combination A1couples not only to O-particles,but also with M-particles with a small charge∝2ε–in other words,mirror matter becomes”milicharged”with respect to the physical ordinary photon2,14.In this way,the term(20)should induce the process e+e−→e′+e′−,with an amplitude just2εtimes the s-channel amplitude for e+e−→e+e−.By this diagram,orthopositronium would oscillate into its mirror counterpart,which would be seen as an invisible decay mode exceeding experimental limits unlessε<5×10−7or so3.c The mirror parity could be spontaneously broken and the weak interaction scales φ =v and φ′ =v′could be different,which leads to somewhat different particle physics in the mirror sector.The models with spontaneoulsy broken parity and their implications were considered in refs.6,9,10.In this paper we mostly concentrate on the case with exact mirror parity.8Zurab BerezhianiFor explaining naturally the smallness of the kinetic mixing term(20)one needsto invoke the concept of grand unification.Obviously,the term(19)is forbiddenif G SM×G′SM is embedded in GUTs like SU(5)×SU(5)′or SO(10)×SO(10)′which do not contain abelian factors.However,given that both SU(5)and SU(5)′symmetries are broken down to their SU(3)×SU(2)×U(1)subgroups by the Higgs24-pletsΦandΦ′,it could emerge from the higher order effective operatorL=−ζ2M (l iφ)(l jφ)+A′ijM(l iφ)(l′jφ′)+h.c.,(22)Thefirst operator in eq.(22),due to the ordinary Higgs vacuum VEV φ =v∼100GeV,then induces the small Majorana masses of the ordinary(active)neutrinos.Since the mirror Higgsφ′also has a non-zero VEV φ′ =v′,the second opera-tor then provides the masses of the M-neutrinos(which in fact are sterile for theordinary observer),andfinally,the third operator induces the mixing mass termsMirror World (9)between the active and sterile neutrinos.The total mass matrix of neutrinosν⊂l andν′⊂l′reads as6:=1Mν= mνmνν′m Tνν′mν′M ab N a N b+h.c.(24)2In this way,N play the role of messengers between ordinary and mirror parti-cles.After integrating out these heavy states,the operators(22)are induced with A=Y G−1Y T,A′=Y′G−1Y′T and D=Y G−1Y′T.In the next section we show that in addition the N states can mediate L and CP violating scattering processes between the O-and M-sectors which could provide a new mechanism for primordial leptogenesis.It is convenient to present the heavy neutrino mass matrix as M ab=G ab M,M being the overall mass scale and G ab some typical Yukawa constants.Without loss of generality,G ab can be taken diagonal and real.Under P or D parities,in general some of the states N a would have positive parity,while others could have a negative one.One the other hand,the Yukawa matrices in general remain non-diagonal and complex.Then D parity would imply that Y′=Y,while P parity imples Y′=Y∗(c.f.(16)and(18)).•Interaction term between the O-and M-Higgses.In the context of G SM×G′SM, the gauge symmetry allows also a quartic interaction term between the O-and M-Higgs doubletsφandφ′:λ(φ†φ)(φ′†φ′)(25) This term is cosmologically dangerous,since it would bring the two sectors into equilibrium in the early Universe via interactions¯φφ→¯φ′φ′unlessλis unnaturally small,λ<10−8.9However,this term can be properly suppressed by supersymmetry.In this case standard Higgsesφu,d become chiral superfields as well as their mirror partners φ′u,d,and so the minimal gauge invariant term between the O-and M-Higgses in the superpotential has dimension5:(1/M)(φuφd)(φ′uφ′d),where M is some big cutoff10Zurab Berezhianimass,e.g.of the order of the GUT scale or Planck scale.Therefore,the general Higgs Lagrangian takes the form:L= d2θ[µφuφd+µφ′uφ′d+1M d2θz(φuφd)(φ′uφ′d)+h.c.,where z=m Sθ2being the supersymmetry break-ing spurion with m S∼100GeV,gives rise to a quartic scalar termλ(φuφd)(φ′uφ′d)+h.c.(28) withλ∼m S/M≪1.Thus forµ,m S∼100GeV,all these quartic constants are strongly suppressed,and hence are safe.•Mixed multiplets between the two sectors.Until now we discussed the situation with O-particles being singlets of mirror gauge factor G′and vice versa,M-particles being singlets of ordinary gauge group G.However,in principle there could be also somefields in mixed representations of G×G′.Suchfields usually emerge if the two gauge factors G and G′are embedded into a bigger grand unification group G.For example,consider a gauge theory SU(5)×SU(5)′where the O-and M-fermions respectively are in the following left-chiral multiplets:L∼(¯5+10,1)and L′∼(1,5+10,Tr[(Y Y′)2](29)3πM2exactly what we expected from the effective operator(21).Hence,the heavy mixed multiplets in fact do not decouple and induce the O-and M-photon kinetic mixingMirror World (11)term proportional to the square of typical mass splittings in these multiplets(∼ Φ 2),analogously to the familiar situation for the photon to Z-boson mixing in the standard model.•Interactions via common gauge bosons.It is pretty possible that O-and M-particles have common forces mediated by the gauge bosons of some additional symmetry group H.In other words,one can consider a theory with a gauge group G×G′×H,where O-particles are in some representations of H,L a∼r a,and correspondingly their antiparticles are in antirepresentations,˜R a∼¯r a.As for M-particles,vice versa,we take L′a∼¯r a,and so˜R′a∼r a.Only such a prescription of G pattern is compatible with the mirror parity(17).In addition,in this case H symmetry automatically becomes vector-like and so it would have no problems with axial anomalies even if the particle contents of O-and M-sectors separately are not anomaly-free with respect to H.Let us consider the following example.The horizontalflavour symmetry SU(3)H between the quark-lepton families seems to be very promising for understanding the fermion mass and mixing pattern21,22.In addition,it can be useful for control-ling theflavour-changing phenomena in the context of supersymmetry7.One can consider e.g.a GUT with SU(5)×SU(3)H symmetry where L-fermions in(6)are triplets of SU(3)H.So SU(3)H has a chiral character and it is not anomaly-free unless some extra states are introduced for the anomaly cancellation21.However,the concept of mirror sector makes the things easier.Consider e.g. SU(5)×SU(5)′×SU(3)H theory with L-fermions in(6)being triplets of SU(3)H while L′-fermions in(11)are anti-triplets.Hence,in this case the SU(3)H anomalies of the ordinary particles are cancelled by their mirror partners.Another advantage is that in a supersymmetric theory the gauge D-terms of SU(3)H are perfectly cancelled between the two sectors and hence they do not give rise to dangerous flavour-changing phenomena7.The immediate implication of such a theory would be the mixing of neutral O-bosons to their M-partners,mediated by horizontal gauge ly,oscil-lationsπ0→π′0or K0→K′0become possible and perhaps even detectable if the horizontal symmetry breaking scale is not too high.Another example is a common lepton number(or B−L)symmetry between the two sectors.Let us assume that ordinary leptons l have lepton charges L=1under this symmetry while mirror ones l′have L=−1.Obviously,this symmetry would forbid thefirst two couplings in(22),A,A′=0,while the third term is allowed–D=0.Hence,‘Majorana’mass terms would be absent both for O-and M-neutrinos in(23)and so neutrinos would be Dirac particles having naturally small masses, with left componentsνL⊂l and right components being˜ν′R⊂˜l.The model with common Peccei-Quinn symmetry between the O-and M-sectors was considered in23.12Zurab Berezhiani3.The expansion of the Universe and thermodynamics of the O-and M-sectorsLet us assume,that after inflation ended,the O-and M-systems received different reheating temperatures,namely T R>T′R.This is certainly possible despite the fact that two sectors have identical Lagrangians,and can be naturally achieved in certain models of inflation8,9,10.dIf the two systems were decoupled already after reheating,at later times t they will have different temperatures T(t)and T′(t),and so different energy and entropy densities:ρ(t)=π230g′∗(T′)T′4,(30)s(t)=2π245g′s(T′)T′3.(31)The factors g∗,g s and g′∗,g′s accounting for the effective number of the degrees of freedom in the two systems can in general be different from each other.Let us assume that during the expansion of the Universe the two sectors evolve with separately conserved entropies.Then the ratio x≡(s′/s)1/3is time independent while the ratio of the temperatures in the two sectors is simply given by:T′(t)g′s(T′) 1/3.(32)The Hubble expansion rate is determined by the total energy density¯ρ=ρ+ρ′, H=2t=1.66 M P l=1.66 M P l(33) in terms of O-and M-temperatures T(t)and T′(t),where¯g∗(T)=g∗(T)(1+x4),¯g′∗(T′)=g′∗(T′)(1+x−4).(34) In particular,we have x=T′0/T0,where T0,T′0are the present temperatures of the O-and M-relic photons.In fact,x is the only free parameter in our model and it is constrained by the BBN bounds.The observed abundances of light elements are in good agreement with the stan-dard nucleosynthesis predictions.At T∼1MeV we have g∗=10.75as it is satu-rated by photonsγ,electrons e and three neutrino speciesνe,µ,τ.The contribution of mirror particles(γ′,e′andν′e,µ,τ)would change it to¯g∗=g∗(1+x4).Deviations from g∗=10.75are usually parametrized in terms of the effective number of extra neutrino species,∆g=¯g∗−10.75=1.75∆Nν.Thus we have:∆Nν=6.14·x4.(35)d For analogy,two harmonic oscillators with the same frequency(e.g.two springs with the same material and the same length)are not obliged to oscillate with the same amplitudes.Mirror World (13)This limit very weakly depends on∆Nν.Namely,the conservative bound∆Nν<1 implies x<0.64.In view of the present observational situation,confronting the WMAP results to the BBN analysis,the bound seems to be stronger.However,e.g. x=0.3implies a completely negligible contribution∆Nν=0.05.As far as x4≪1,in a relativistic epoch the Hubble expansion rate(33)is dominated by the O-matter density and the presence of the M-sector practically does not affect the standard cosmology of the early ordinary Universe.However, even if the two sectors have the same microphysics,the cosmology of the early mirror world can be very different from the standard one as far as the crucial epochs like baryogenesis,nuclesosynthesis,etc.are concerned.Any of these epochs is related to an instant when the rate of the relevant particle processΓ(T),which is generically a function of the temperature,becomes equal to the Hubble expansion rate H(T).Obviously,in the M-sector these events take place earlier than in the O-sector,and as a rule,the relevant processes in the former freeze out at larger temperatures than in the latter.In the matter domination epoch the situation becomes different.In particular, we know that ordinary baryons provide only a small fraction of the present matter density,whereas the observational data indicate the presence of dark matter with about5times larger density.It is interesting to question whether the missing matter density of the Universe could be due to mirror baryons?In the next section we show that this could occur in a pretty natural manner.It can also be shown that the BBN epoch in the mirror world proceeds differ-ently from the ordinary one,and it predicts different abundancies of primordial ly,mirror helium abundance can be in the range Y′4=0.6−0.8, considerably larger than the observable Y4≃0.24.4.Baryogenesis in M-sector and mirror baryons as dark matter4.1.Visible and dark matter in the UniverseThe present cosmological observations strongly support the main predictions of the inflationary scenario:first,the Universe isflat,with the energy density very close to the criticalΩ=1,and second,primoridal density perturbations have nearlyflat spectrum,with the spectral index n s≈1.The non-relativistic matter gives only a small fraction of the present energy density,aboutΩm≃0.27,while the rest is attributed to the vacuum energy(cosmological term)ΩΛ≃0.7324.The fact that Ωm andΩΛare of the same order,gives rise to so called cosmological coincidence problem:why we live in an epoch whenρm∼ρλ,if in the early Universe one had ρm≫ρΛand in the late Universe one would expectρm≪ρΛ?The answer can be only related to an antrophic principle:the matter and vacuum energy densities scale differently with the expansion of the Universeρm∝a−3andρΛ∝const., hence they have to coincide at some moment,and we are just happy to be here. Moreover,for substantially largerρΛno galaxies could be formed and thus there would not be anyone to ask this this question.14Zurab BerezhianiOn the other hand,the matter in the Universe has two components,visible and dark:Ωm=Ωb+Ωd.The visible matter consists of baryons withΩb≃0.044while the dark matter withΩd≃0.22is constituted by some hypothetic particle species very weakly interacting with the observable matter.It is a tantalizing question,why the visible and dark components have so close energy densities?Clearly,the ratioρdβ=Mirror World (15)the O-baryon density n b.Thus,one could question whether the ratioβ=n′b/n bcould be naturally order1or somewhat bigger.The visible matter in the Universe consists of baryons,while the abundance ofantibaryons is vanishingly small.In the early Universe,at tempreatures T≫1GeV,the baryons and antibaryons had practically the same densities,n b≈n¯b with n b slightly exceeding n¯b,so that the baryon number density was small,n B=n b−n¯b≪n b.If there was no significant entropy production after the baryogenesis epoch,the baryon number density to entropy density ratio had to be the same as today,B=n B/s≈8×10−11.eOne can question,who and how has prepared the initial Universe with sucha small excess of baryons over antibaryons.In the Friedman Universe the initialbaryon asymmetry could be arranged a priori,in terms of non-vanishing chemicalpotential of baryons.However,the inflationary paradigm gives another twist to thisquestion,since inflation dilutes any preexisting baryon number of the Universe tozero.Therefore,after inflaton decay and the(re-)heating of the Universe,the baryonasymmetry has to be created by some cosmological mechanism.There are several relatively honest baryogenesis mechanisms as are GUT baryo-genesis,leptogenesis,electroweak baryogenesis,etc.(for a review,see e.g.25).Theyare all based on general principles suggested long time ago by Sakharov26:a non-zero baryon asymmetry can be produced in the initially baryon symmetric Universeif three conditions are fulfilled:B-violation,C-and CP-violation and departurefrom thermal equilibrium.In the GUT baryogenesis or leptogenesis scenarios theseconditions can be satisfied in the decays of heavy particles.At present it is not possible to say definitely which of the known mechanisms isresponsible for the observed baryon asymmetry in the ordinary world.However,it ismost likely that the baryon asymmetry in the mirror world is produced by the samemechanism and moreover,the properties of the B and CP violation processes areparametrically the same in both cases.But the mirror sector has a lower temperaturethan ordinary one,and so at epochs relevant for baryogenesis the out-of-equilibriumconditions should be easier fulfilled for the M-sector.4.2.Baryogenesis in the O-and M-worldsLet us consider the difference between the ordinary and mirror baryon asymme-tries on the example of the GUT baryogenesis mechanism.It is typically basedon‘slow’B-and CP-violating decays of a superheavy boson X into quarks andleptons,where slow means that at T<M the Hubble parameter H(T)is greaterthan the decay rateΓ∼αM,αbeing the coupling strength of X to fermionsand M its mass.The other reaction rates are also of relevance:inverse decay:ΓI∼Γ(M/T)3/2exp(−M/T)for T<M X,and the X boson mediated scatteringe In the following we use B=n B/s which is related with the familiarη=n B/nγas B≈0.14η. However,B is more adopted for featuring the baryon asymmetry since it does not depend on time if the entropy of the Universe is conserved.。