Quantum measurements and the Abelian Stabilizer Problem

清华考博辅导：清华大学计算机科学与技术考博难度解析及经验分享根据教育部学位与研究生教育发展中心最新公布的第四轮学科评估结果可知，全国共有168所开设计算机科学与技术专业的大学参与了2017-2018计算机科学与技术专业大学排名，其中排名第一的是北京大学，排名第二的是清华大学，排名第三的是浙江大学。

作为清华大学实施国家“211工程”和“985工程”的重点学科，计算机科学与技术一级学科在历次全国学科评估中均名列第二。

下面是启道考博整理的关于清华大学计算机科学与技术考博相关内容。

一、专业介绍计算机科学与技术是研究计算机的设计与制造，并利用计算机进行有关的信息表示、收发、存储、处理、控制等的理论方法和技术的学科。

计算机专业涵盖计算机科学与技术、计算机软件工程、计算机信息工程等专业，主要培养具有良好的科学素养，系统地、较好地掌握计算机科学与技术，包括计算机硬件和软件组成原理、计算机操作系统、计算机网络基础、算法与数据结构等，计算机的基本知识和基本技能与方法，能在科研部门、教育、企业、事业、行政管理部门等单位从事计算机教学、科学研究和计算机科学与技术学科的应用。

清华大学计算机科学与技术专业在博士招生方面，划分为3个研究方向：081200计算机科学与技术研究方向：01信息安全；02机器智能；03金融科技；04网络科学；05计算生物学；06能源信息科学；07机器人；08理论计算机科学；09量子信息此专业实行申请考核制。

二、考试内容清华大学计算机科学与技术专业博士研究生招生为资格审查加综合考核形式，由笔试+面试构成。

其中，综合考核内容为:综合考核形式为面试：每位考生约30 分钟，满分100 分。

面试重点考查申请人在本学科攻读博士学位的基本素养、学术能力、学术志趣等。

三、时间安排1.博士生申请在每年的8-9月和11月。

2.直博生（包括夏令营拟录取的直博生）、硕博连读生及部分9月份招收普博生的院系8-9月申请，9月中下旬考试录取，见当年招生简章及目录、招生说明、直博直硕招生要求。

九年级英语名人传记阅读理解与启示提炼单选题50题1. Albert Einstein is famous for his theory of relativity. Which of the following was one of his early achievements in his scientific career?A. Discovering the law of gravityB. Proposing the photoelectric effect theoryC. Inventing the electric lightD. Finding a cure for a certain disease答案：B。

解析：爱因斯坦早期提出了光电效应理论。

A选项发现万有引力定律的是牛顿；C选项发明电灯的是爱迪生；D选项爱因斯坦没有在疾病治疗方面有相关成就，这些错误选项都是混淆了不同科学家的成就。

2. Marie Curie was the first woman to win a Nobel Prize. What was the field of her research mainly about?A. BiologyB. Chemistry and radioactivityC. Physics of soundD. Astronomy答案：B。

解析：居里夫人的研究领域主要是化学和放射性。

A选项生物学不是居里夫人的主要研究领域；C选项声学物理与居里夫人的研究无关；D选项天文学也不是居里夫人的研究方向，这些错误选项都是与居里夫人的实际研究领域不相符的内容。

3. Isaac Newton made great contributions to science. What inspiredhim to study gravity?A. A falling appleB. A flying birdC. A running horseD. A floating cloud答案：A。

量子力学英文读物以下是一些关于量子力学的英文读物推荐：1. "Quantum: Einstein, Bohr, and the Great Debate about the Nature of Reality" by Manjit Kumar2. "The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory" by Brian Greene3. "The Quantum World: Quantum Physics for Everyone" by Kenneth W. Ford4. "Quantum Mechanics: Concepts and Applications" by Nouredine Zettili5. "Quantum Physics: A Beginner's Guide" by Alastair Rae6. "Quantum Computing for Computer Scientists" by Noson S. Yanofsky and Mirco A. Mannucci7. "Quantum Physics for Babies" by Chris Ferrie (a simplified introduction for children and adults)8. "The Strange World of Quantum Mechanics" by Daniel F. Styer这些书籍从不同的角度介绍了量子力学的基本原理、应用、历史以及相关的思想争论。

根据你的兴趣和程度，选择适合你的读物开始探索量子世界吧！。

21-centimeter line, 21厘米线AAbsorption, 吸收Addition of angular momenta, 角动量叠加Adiabatic approximation, 绝热近似Adiabatic process, 绝热过程Adjoint, 自伴的Agnostic position, 不可知论立场Aharonov-Bohm effect, 阿哈罗诺夫-玻姆效应Airy equation, 艾里方程；Airy function, 艾里函数Allowed energy, 允许能量Allowed transition, 允许跃迁Alpha decay, 衰变；Alpha particle, 粒子Angular equation, 角向方程Angular momentum, 角动量Anomalous magnetic moment, 反常磁矩Antibonding, 反键Anti-hermitian operator, 反厄米算符Associated Laguerre polynomial, 连带拉盖尔多项式Associated Legendre function, 连带勒让德多项式Atoms, 原子Average value, 平均值Azimuthal angle, 方位角Azimuthal quantum number, 角量子数BBalmer series, 巴尔末线系Band structure, 能带结构Baryon, 重子Berry's phase, 贝利相位Bessel functions, 贝塞尔函数Binding energy, 束缚能Binomial coefficient, 二项式系数Biot-Savart law, 毕奥-沙法尔定律Blackbody spectrum, 黑体谱Bloch's theorem, 布洛赫定理Bohr energies, 玻尔能量；Bohr magneton, 玻尔磁子；Bohr radius, 玻尔半径Boltzmann constant, 玻尔兹曼常数Bond, 化学键Born approximation, 玻恩近似Born's statistical interpretation, 玻恩统计诠释Bose condensation, 玻色凝聚Bose-Einstein distribution, 玻色-爱因斯坦分布Boson, 玻色子Bound state, 束缚态Boundary conditions, 边界条件Bra, 左矢Bulk modulus, 体积模量CCanonical commutation relations, 正则对易关系Canonical momentum, 正则动量Cauchy's integral formula, 柯西积分公式Centrifugal term, 离心项Chandrasekhar limit, 钱德拉赛卡极限Chemical potential, 化学势Classical electron radius, 经典电子半径Clebsch-Gordan coefficients, 克-高系数Coherent States, 相干态Collapse of wave function, 波函数塌缩Commutator, 对易子Compatible observables, 对易的可观测量Complete inner product space, 完备内积空间Completeness, 完备性Conductor, 导体Configuration, 位形Connection formulas, 连接公式Conservation, 守恒Conservative systems, 保守系Continuity equation, 连续性方程Continuous spectrum, 连续谱Continuous variables, 连续变量Contour integral, 围道积分Copenhagen interpretation, 哥本哈根诠释Coulomb barrier, 库仑势垒Coulomb potential, 库仑势Covalent bond, 共价键Critical temperature, 临界温度Cross-section, 截面Crystal, 晶体Cubic symmetry, 立方对称性Cyclotron motion, 螺旋运动DDarwin term, 达尔文项de Broglie formula, 德布罗意公式de Broglie wavelength, 德布罗意波长Decay mode, 衰变模式Degeneracy, 简并度Degeneracy pressure, 简并压Degenerate perturbation theory, 简并微扰论Degenerate states, 简并态Degrees of freedom, 自由度Delta-function barrier, 势垒Delta-function well, 势阱Derivative operator, 求导算符Determinant, 行列式Determinate state, 确定的态Deuterium, 氘Deuteron, 氘核Diagonal matrix, 对角矩阵Diagonalizable matrix, 对角化Differential cross-section, 微分截面Dipole moment, 偶极矩Dirac delta function, 狄拉克函数Dirac equation, 狄拉克方程Dirac notation, 狄拉克记号Dirac orthonormality, 狄拉克正交归一性Direct integral, 直接积分Discrete spectrum, 分立谱Discrete variable, 离散变量Dispersion relation, 色散关系Displacement operator, 位移算符Distinguishable particles, 可分辨粒子Distribution, 分布Doping, 掺杂Double well, 双势阱Dual space, 对偶空间Dynamic phase, 动力学相位EEffective nuclear charge, 有效核电荷Effective potential, 有效势Ehrenfest's theorem, 厄伦费斯特定理Eigenfunction, 本征函数Eigenvalue, 本征值Eigenvector, 本征矢Einstein's A and B coefficients, 爱因斯坦A,B系数；Einstein's mass-energy formula, 爱因斯坦质能公式Electric dipole, 电偶极Electric dipole moment, 电偶极矩Electric dipole radiation, 电偶极辐射Electric dipole transition, 电偶极跃迁Electric quadrupole transition, 电四极跃迁Electric field, 电场Electromagnetic wave, 电磁波Electron, 电子Emission, 发射Energy, 能量Energy-time uncertainty principle, 能量-时间不确定性关系Ensemble, 系综Equilibrium, 平衡Equipartition theorem, 配分函数Euler's formula, 欧拉公式Even function, 偶函数Exchange force, 交换力Exchange integral, 交换积分Exchange operator, 交换算符Excited state, 激发态Exclusion principle, 不相容原理Expectation value, 期待值FFermi-Dirac distribution, 费米-狄拉克分布Fermi energy, 费米能Fermi surface, 费米面Fermi temperature, 费米温度Fermi's golden rule, 费米黄金规则Fermion, 费米子Feynman diagram, 费曼图Feynman-Hellman theorem, 费曼-海尔曼定理Fine structure, 精细结构Fine structure constant, 精细结构常数Finite square well, 有限深方势阱First-order correction, 一级修正Flux quantization, 磁通量子化Forbidden transition, 禁戒跃迁Foucault pendulum, 傅科摆Fourier series, 傅里叶级数Fourier transform, 傅里叶变换Free electron, 自由电子Free electron density, 自由电子密度Free electron gas, 自由电子气Free particle, 自由粒子Function space, 函数空间Fusion, 聚变Gg-factor, g-因子Gamma function, 函数Gap, 能隙Gauge invariance, 规范不变性Gauge transformation, 规范变换Gaussian wave packet, 高斯波包Generalized function, 广义函数Generating function, 生成函数Generator, 生成元Geometric phase, 几何相位Geometric series, 几何级数Golden rule, 黄金规则"Good" quantum number, "好"量子数"Good" states, "好"的态Gradient, 梯度Gram-Schmidt orthogonalization, 格莱姆-施密特正交化法Graphical solution, 图解法Green's function, 格林函数Ground state, 基态Group theory, 群论Group velocity, 群速Gyromagnetic railo, 回转磁比值HHalf-integer angular momentum, 半整数角动量Half-life, 半衰期Hamiltonian, 哈密顿量Hankel functions, 汉克尔函数Hannay's angle, 哈内角Hard-sphere scattering, 硬球散射Harmonic oscillator, 谐振子Heisenberg picture, 海森堡绘景Heisenberg uncertainty principle, 海森堡不确定性关系Helium, 氦Helmholtz equation, 亥姆霍兹方程Hermite polynomials, 厄米多项式Hermitian conjugate, 厄米共轭Hermitian matrix, 厄米矩阵Hidden variables, 隐变量Hilbert space, 希尔伯特空间Hole, 空穴Hooke's law, 胡克定律Hund's rules, 洪特规则Hydrogen atom, 氢原子Hydrogen ion, 氢离子Hydrogen molecule, 氢分子Hydrogen molecule ion, 氢分子离子Hydrogenic atom, 类氢原子Hyperfine splitting, 超精细分裂IIdea gas, 理想气体Idempotent operaror, 幂等算符Identical particles, 全同粒子Identity operator, 恒等算符Impact parameter, 碰撞参数Impulse approximation, 脉冲近似Incident wave, 入射波Incoherent perturbation, 非相干微扰Incompatible observables, 不对易的可观测量Incompleteness, 不完备性Indeterminacy, 非确定性Indistinguishable particles, 不可分辨粒子Infinite spherical well, 无限深球势阱Infinite square well, 无限深方势阱Inner product, 内积Insulator, 绝缘体Integration by parts, 分部积分Intrinsic angular momentum, 内禀角动量Inverse beta decay, 逆衰变Inverse Fourier transform, 傅里叶逆变换KKet, 右矢Kinetic energy, 动能Kramers' relation, 克莱默斯关系Kronecker delta, 克劳尼克LLCAO technique, 原子轨道线性组合法Ladder operators, 阶梯算符Lagrange multiplier, 拉格朗日乘子Laguerre polynomial, 拉盖尔多项式Lamb shift, 兰姆移动Lande g-factor, 朗德g-因子Laplacian, 拉普拉斯的Larmor formula, 拉摩公式Larmor frequency, 拉摩频率Larmor precession, 拉摩进动Laser, 激光Legendre polynomial, 勒让德多项式Levi-Civita symbol, 列维-西维塔符号Lifetime, 寿命Linear algebra, 线性代数Linear combination, 线性组合Linear combination of atomic orbitals, 原子轨道的线性组合Linear operator, 线性算符Linear transformation, 线性变换Lorentz force law, 洛伦兹力定律Lowering operator, 下降算符Luminoscity, 照度Lyman series, 赖曼线系MMagnetic dipole, 磁偶极Magnetic dipole moment, 磁偶极矩Magnetic dipole transition, 磁偶极跃迁Magnetic field, 磁场Magnetic flux, 磁通量Magnetic quantum number, 磁量子数Magnetic resonance, 磁共振Many worlds interpretation, 多世界诠释Matrix, 矩阵；Matrix element, 矩阵元Maxwell-Boltzmann distribution, 麦克斯韦-玻尔兹曼分布Maxwell's equations, 麦克斯韦方程Mean value, 平均值Measurement, 测量Median value, 中位值Meson, 介子Metastable state, 亚稳态Minimum-uncertainty wave packet, 最小不确定度波包Molecule, 分子Momentum, 动量Momentum operator, 动量算符Momentum space wave function, 动量空间波函数Momentum transfer, 动量转移Most probable value, 最可几值Muon, 子Muon-catalysed fusion, 子催化的聚变Muonic hydrogen, 原子Muonium, 子素NNeumann function, 纽曼函数Neutrino oscillations, 中微子振荡Neutron star, 中子星Node, 节点Nomenclature, 术语Nondegenerate perturbationtheory, 非简并微扰论Non-normalizable function, 不可归一化的函数Normalization, 归一化Nuclear lifetime, 核寿命Nuclear magnetic resonance, 核磁共振Null vector, 零矢量OObservable, 可观测量Observer, 观测者Occupation number, 占有数Odd function, 奇函数Operator, 算符Optical theorem, 光学定理Orbital, 轨道的Orbital angular momentum, 轨道角动量Orthodox position, 正统立场Orthogonality, 正交性Orthogonalization, 正交化Orthohelium, 正氦Orthonormality, 正交归一性Orthorhombic symmetry, 斜方对称Overlap integral, 交叠积分PParahelium, 仲氦Partial wave amplitude, 分波幅Partial wave analysis, 分波法Paschen series, 帕邢线系Pauli exclusion principle, 泡利不相容原理Pauli spin matrices, 泡利自旋矩阵Periodic table, 周期表Perturbation theory, 微扰论Phase, 相位Phase shift, 相移Phase velocity, 相速Photon, 光子Planck's blackbody formula, 普朗克黑体辐射公式Planck's constant, 普朗克常数Polar angle, 极角Polarization, 极化Population inversion, 粒子数反转Position, 位置；Position operator, 位置算符Position-momentum uncertainty principles, 位置-动量不确定性关系Position space wave function, 坐标空间波函数Positronium, 电子偶素Potential energy, 势能Potential well, 势阱Power law potential, 幂律势Power series expansion, 幂级数展开Principal quantum number, 主量子数Probability, 几率Probability current, 几率流Probability density, 几率密度Projection operator, 投影算符Propagator, 传播子Proton, 质子QQuantum dynamics, 量子动力学Quantum electrodynamics, 量子电动力学Quantum number, 量子数Quantum statics, 量子统计Quantum statistical mechanics, 量子统计力学Quark, 夸克RRabi flopping frequency, 拉比翻转频率Radial equation, 径向方程Radial wave function, 径向波函数Radiation, 辐射Radius, 半径Raising operator, 上升算符Rayleigh's formula, 瑞利公式Realist position, 实在论立场Recursion formula, 递推公式Reduced mass, 约化质量Reflected wave, 反射波Reflection coefficient, 反射系数Relativistic correction, 相对论修正Rigid rotor, 刚性转子Rodrigues formula, 罗德里格斯公式Rotating wave approximation, 旋转波近似Rutherford scattering, 卢瑟福散射Rydberg constant, 里德堡常数Rydberg formula, 里德堡公式SScalar potential, 标势Scattering, 散射Scattering amplitude, 散射幅Scattering angle, 散射角Scattering matrix, 散射矩阵Scattering state, 散射态Schrodinger equation, 薛定谔方程Schrodinger picture, 薛定谔绘景Schwarz inequality, 施瓦兹不等式Screening, 屏蔽Second-order correction, 二级修正Selection rules, 选择定则Semiconductor, 半导体Separable solutions, 分离变量解Separation of variables, 变量分离Shell, 壳Simple harmonic oscillator, 简谐振子Simultaneous diagonalization, 同时对角化Singlet state, 单态Slater determinant, 斯拉特行列式Soft-sphere scattering, 软球散射Solenoid, 螺线管Solids, 固体Spectral decomposition, 谱分解Spectrum, 谱Spherical Bessel functions, 球贝塞尔函数Spherical coordinates, 球坐标Spherical Hankel functions, 球汉克尔函数Spherical harmonics, 球谐函数Spherical Neumann functions, 球纽曼函数Spin, 自旋Spin matrices, 自旋矩阵Spin-orbit coupling, 自旋-轨道耦合Spin-orbit interaction, 自旋-轨道相互作用Spinor, 旋量Spin-spin coupling, 自旋-自旋耦合Spontaneous emission, 自发辐射Square-integrable function, 平方可积函数Square well, 方势阱Standard deviation, 标准偏差Stark effect, 斯塔克效应Stationary state, 定态Statistical interpretation, 统计诠释Statistical mechanics, 统计力学Stefan-Boltzmann law, 斯特番-玻尔兹曼定律Step function, 阶跃函数Stem-Gerlach experiment, 斯特恩-盖拉赫实验Stimulated emission, 受激辐射Stirling's approximation, 斯特林近似Superconductor, 超导体Symmetrization, 对称化Symmetry, 对称TTaylor series, 泰勒级数Temperature, 温度Tetragonal symmetry, 正方对称Thermal equilibrium, 热平衡Thomas precession, 托马斯进动Time-dependent perturbation theory, 含时微扰论Time-dependent Schrodinger equation, 含时薛定谔方程Time-independent perturbation theory, 定态微扰论Time-independent Schrodinger equation, 定态薛定谔方程Total cross-section, 总截面Transfer matrix, 转移矩阵Transformation, 变换Transition, 跃迁；Transition probability, 跃迁几率Transition rate, 跃迁速率Translation,平移Transmission coefficient, 透射系数Transmitted wave, 透射波Trial wave function, 试探波函数Triplet state, 三重态Tunneling, 隧穿Turning points, 回转点Two-fold degeneracy , 二重简并Two-level systems, 二能级体系UUncertainty principle, 不确定性关系Unstable particles, 不稳定粒子VValence electron, 价电子Van der Waals interaction, 范德瓦尔斯相互作用Variables, 变量Variance, 方差Variational principle, 变分原理Vector, 矢量Vector potential, 矢势Velocity, 速度Vertex factor, 顶角因子Virial theorem, 维里定理WWave function, 波函数Wavelength, 波长Wave number, 波数Wave packet, 波包Wave vector, 波矢White dwarf, 白矮星Wien's displacement law, 维恩位移定律YYukawa potential, 汤川势ZZeeman effect, 塞曼效应。

量子力学英文介绍Quantum mechanics, also known as quantum physics, is a branch of theoretical physics that describes the behavior of matter and energy at the smallest scales, including subatomic particles like electrons and photons. It is an incredibly complex and counterintuitive theory, but also one of the most successful scientific theories ever developed.Step 1: The Beginnings of Quantum MechanicsQuantum mechanics originated in the early 20th century, primarily through the work of physicists Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, and ErwinSchrödinger. Their investigations into the behavior of light and matter led them to develop a new set of mathematical equations that governed the behavior of subatomic particles.Step 2: The Weirdness of Quantum MechanicsQuantum mechanics has a number of strange and seemingly paradoxical features that make it hard to wrap one's head around. For example, particles at the quantum level do not have a definite location until they are measured, and they can exist in multiple states at once. Quantum mechanics also introduced the concept of entanglement, in which particles can become "entangled" so that a measurement of one particle can instantly affect the state of the other, even if they are separated by vast distances.Step 3: Applications of Quantum MechanicsDespite its weirdness, quantum mechanics has a wide range of practical applications. One of the most notable is the development of the transistor, which is a crucialcomponent in modern electronic devices like computers and smartphones. Quantum mechanics also plays a role in materials science, cryptography, and quantum computing, which has the potential to revolutionize computation.Step 4: Current Research in Quantum MechanicsQuantum mechanics continues to be an active area of research and discovery. Areas of current interest include quantum entanglement and teleportation, the development of more efficient quantum algorithms, and exploring the possibilities of quantum computing. Researchers are also investigating the relationship between quantum mechanics and general relativity, the other pillar of modern physics.In conclusion, quantum mechanics is a fascinating and important theory that has revolutionized our understanding of the universe. It has many practical applications and continues to inspire new discoveries and innovations. While its weirdness and complexity can be daunting, it is well worth the effort to understand and appreciate this amazing theory.。

有关量子力学的英语作文Quantum mechanics is a branch of physics that deals with the behavior of very small particles, such as atoms and subatomic particles.It's a mind-boggling theory that challenges our understanding of the universe and how things work at the most fundamental level.Quantum mechanics has led to the development of many important technologies, such as lasers, transistors, and MRI machines.One of the most famous principles of quantum mechanics is the Heisenberg Uncertainty Principle, which states that it is impossible to simultaneously know the exact position and momentum of a particle.Quantum mechanics also introduces the concept of superposition, which means that particles can exist inmultiple states at the same time.Another fascinating aspect of quantum mechanics is entanglement, where particles become connected in such away that the state of one particle is instantly correlated with the state of another, no matter how far apart they are.Despite its incredible success in explaining the behavior of particles at the quantum level, quantum mechanics is still not fully understood, and many of its implications are still being explored by physicists.The strange and counterintuitive nature of quantum mechanics has led to many debates and discussions about its philosophical and metaphysical implications.。

Quantum FieldsN.N.BogoliubovD.V.ShirkovJo i nt Institutefor Nuclear ResearchDubna,U.S.S.R.Authonrized translation from the Russian edition byD.B.Pontecorvo1983The Benjamin Cummings Publishing Company,Inc.Advanced Book ProgramReading,MassachusettsLondon Amsterdam Don Mills Ontario Sydney Tokyoviii Contents20.The Feynman rules i n the p-representation184201Transition to the momentum representation18420:2Feynman 's rules for the evaluation of elements18820.3An illustration forthe model18720.4Spinor electrodynamics18921.Transition probabilities19321.1The general structure of matrix elements19321.2Normalization of the state amplitude19521.3The general fonnula for transition probability19721.4Scattering of two particles19921.5The two-particle decay202Chapter VI.Evaluation of Integrals and Divergences20322.The method for evaluating integrals20322.1Integrals over virtual momenta20322.2The a-representation and Gaussian quadratures20422.3Feynman's parametrization20722.4Ultraviolet divergences20923.Auxiliary regularizations21023.1The necessity of regularization21023.2Pauli-Villars regularization21123.3D i mensionai regularization21323.4Regularization by means of a cutoff21524.One -loop diagrams21624.1The scalar "fish"21624.2Self-energies of the photon and of the electron21824.3Triangular diagrams22124.4Ultraviolet divergences of higher orders 22325.Isolation of the divergences22525.1The structure of one-loop divergences22525.2The contribution to the S-matrix22625.3Counterterms and renormalizations22925.4Divergences and distributions231Chapter VII .Removal of Divergences23326.The general structure of divergences23326.1divergences23326.2The connection with countertenns and renormalizations23626.3The degree of divergence of diagrams23826.4The property of renonnalizabilit 24027.Dressed Green's functions24227.1Propagators of physical fields24227.2Higher Green 's functions 245Matrix the vertex Higher-orderContents xi "September"Assignment(for Chapter I)365 "October"Assignment(for Chapter II)369 "November"Assignment(for Chapter III)372 "December"Assignment(for Chapter IV)375 "February"Assignment(for Chapter V)376 "March"Assignment(for Chapter VI)378 "April"Assignment(for Chapter VII)379Recommendations for Use381References383 Subject Index..385PREFACEThe main purpose of this book is to provide graduate students in physicswith the necessary minimum of infonnation on the fundament~sof modem quantum field theory.It may tum out to be sufficient both for theoreticians,specializing in nuclear physics,quantum statistics and other fields,in which quantum field methods are utilized and which are based on quantum concepts,and also for experimental physicists in the fields of nuclear and high-energy physics.For the latter category of readers the present book should be supplemented by a course on particle physics and particle interactions.At the same time the book can be recommended as an introductury text for persons intending to work in the field of quantum field theory and of the theory of elementary interactions.The material in this book corresponds to a course lasting one academic year.Our personal experience testifies that parallel practical studies at seminars are extremely desirable.For this purpose part of the technical material has been assembled at the end of the book in the fo rm of Appendices.There,also,sets of exercises and problems,gathered together as assignments corresponding to chapters of the main text,are given.The authors are grateful to the editor of this book D.A.Slavnov,to thereviewers M.A.Brown,L.V.Prokhorov,K.A.Ter~Martirosyan,and also to B.M.Barbashov,B.V.Medvediev,and N.M.Shumeiko for valuable comments on the typescript of the book.N.N.BogoliubovD.V.Shirkovfundamentals Ter-MartirosyanPREFACE TO THEENGLISH-LANGUAGE EDITION This book is a text on the fundamentals of quantum field theory and renormalized perturbation theory(RPT).The traditional field of application of the latter for a long time was limited to quantum electrodynamics.During recent years,due to the creation of a unified theory of electroweak interac-tions and to the successes of quantum chromodynamics it has become clear that the physical scope of RPT is much wider.However,in the study of the quark-gluon interaction,as well as of possible mechanisms of the grand unification of interactions,a decisive partis played by the simultaneous use of results of RPT and of the apparatus of the renormalization-group method.Therefore we have written a special Appendix IX,"The renormaliza-tion group,"for the English-language edition of our book.Besides this,small editorial changes and corrections of noticed misprints have been made.N.N.BogoliubovD.V.Shirkovxv。

量子力学的英语Quantum mechanics is a fascinating branch of physics that explores the behavior of particles at the smallest scales. It delves into the realm of atoms and subatomic particles, revealing a world where the laws of classical physics no longer apply.At its core, quantum mechanics challenges our everyday understanding of reality. It introduces concepts such as superposition, where particles can exist in multiple states simultaneously, and entanglement, a mysterious connection between particles that Einstein famously referred to as "spooky action at a distance."The implications of quantum mechanics are profound, impacting not just our understanding of the universe but also the development of technologies like quantum computing. It's a field that continues to push the boundaries of what we know and how we think about the world around us.Despite its complexity, the principles of quantum mechanics can be grasped even by those new to the subject.It's a testament to the beauty of science that such intricate concepts can be understood and appreciated by curious minds of all ages.In essence, quantum mechanics is more than just a scientific theory; it's a window into the very fabric of ourexistence, offering a glimpse into the fundamental nature of reality that is both humbling and awe-inspiring.。

自旋全同粒子自旋是描述粒子的一种性质，它是量子力学中旋转不变性的内禀表示。

在自旋理论中，粒子根据自旋量子数的不同可以分为整数自旋粒子（如光子、重整数自旋粒子（如电子）、半整数自旋粒子（如中子）等。

自旋全同粒子是指具有相同自旋量子数的粒子，它们在物理理论和实验研究中具有很重要的地位。

根据量子力学的统计原理，自旋全同粒子的波函数必须满足对称或反对称的交换关系。

对于玻色子（具有整数自旋）的自旋全同粒子，它们的波函数必须是对称的；而对于费米子（具有半整数自旋）的自旋全同粒子，它们的波函数必须是反对称的。

自旋全同粒子的理论研究在原子、分子、凝聚态物理以及量子信息等领域有很广泛的应用。

以下是一些相关的参考内容：1. 书籍：- 《Quantum Mechanics: Concepts and Applications》（Nouredine Zettili）- 《Quantum Mechanics: Concepts and Applications》（Nouredine Zettili）- 《Quantum Mechanics and Path Integrals》（Richard P. Feynman, Albert R. Hibbs）- 《Group Theory in Physics: An Introduction》（J. F. Cornwell）- 《Modern Quantum Mechanics》（J. J. Sakurai, Jim Napolitano）这些书籍涵盖了自旋理论及其应用的基本概念、数学形式和物理解释等方面的内容。

2. 研究论文：- "Non-Abelian anyons and topological quantum computation"（A. Y. Kitaev）- "Spin and Statistics of Quantum Particles in Two Dimensions"（F. Wilczek）- "Topological Quantum Computation and Anyonic Interferometry"（Chetan Nayak et al）- "Quantum Coherence and Pauli Spin Matrices"（S. A. Gurvitz）这些研究论文介绍了自旋全同粒子在拓扑量子计算、任意子干涉等领域的理论研究和可能的应用。