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量子多体系统的理论模型引言量子力学是描述微观物质行为的基本理论。
在量子力学中，描述一个系统的基本单位是量子态，而量子多体系统则是由多个量子态组成的系统。
由于量子多体系统的复杂性，需要借助一些理论模型来描述和研究。
本文将介绍一些常见的量子多体系统的理论模型，包括自旋链模型、玻色-爱因斯坦凝聚模型和费米气体模型等。
通过对这些模型的研究，我们可以深入了解量子多体系统的行为和性质。
自旋链模型自旋链模型是描述自旋之间相互作用的量子多体系统的模型。
在自旋链模型中，每个粒子可以处于自旋向上或向下的两种状态。
粒子之间通过自旋-自旋相互作用产生相互作用。
常见的自旋链模型包括Ising模型和Heisenberg模型。
Ising模型Ising模型是最简单的自旋链模型之一。
在一维Ising模型中，每个自旋可以取向上（+1）或向下（-1）。
自旋之间通过简单的相邻自旋相互作用来影响彼此的取向。
可以使用以下哈密顿量来描述一维Ising模型：$$H = -J\\sum_{i=1}^{N}s_is_{i+1}$$其中，J为相邻自旋之间的交换耦合常数，s i为第i个自旋的取向。
Heisenberg模型Heisenberg模型是描述自旋间相互作用的模型，与Ising模型不同的是，Heisenberg模型中的自旋可以沿任意方向取向。
常见的一维Heisenberg模型可以使用以下哈密顿量来描述：$$H = \\sum_{i=1}^{N} J\\mathbf{S}_i \\cdot \\mathbf{S}_{i+1}$$其中，$\\mathbf{S}_i$为第i个自旋的自旋算符，J为自旋间的交换耦合常数。
玻色-爱因斯坦凝聚模型玻色-爱因斯坦凝聚是一种量子多体系统的现象，它描述了玻色子统计的粒子在低温下向基态排列的行为。
玻色-爱因斯坦凝聚模型可以使用用薛定谔方程来描述：$$i\\hbar\\frac{\\partial}{\\partial t}\\Psi(\\mathbf{r},t) = -\\frac{\\hbar^2}{2m}\ abla^2\\Psi(\\mathbf{r},t) +V(\\mathbf{r})\\Psi(\\mathbf{r},t) +g|\\Psi(\\mathbf{r},t)|^2\\Psi(\\mathbf{r},t)$$其中，$\\Psi(\\mathbf{r},t)$是波函数，m是粒子的质量，$V(\\mathbf{r})$是外势场，g是粒子之间的相互作用常数。
多种群混沌映射麻雀优化算法下载温馨提示：该文档是我店铺精心编制而成，希望大家下载以后，能够帮助大家解决实际的问题。
文档下载后可定制随意修改，请根据实际需要进行相应的调整和使用，谢谢!并且，本店铺为大家提供各种各样类型的实用资料，如教育随笔、日记赏析、句子摘抄、古诗大全、经典美文、话题作文、工作总结、词语解析、文案摘录、其他资料等等，如想了解不同资料格式和写法，敬请关注!Download tips: This document is carefully compiled by the editor. I hope that after you download them, they can help yousolve practical problems. The document can be customized and modified after downloading, please adjust and use it according to actual needs, thank you!In addition, our shop provides you with various types of practical materials, such as educational essays, diary appreciation, sentence excerpts, ancient poems, classic articles, topic composition, work summary, word parsing, copy excerpts,other materials and so on, want to know different data formats and writing methods, please pay attention!多种群混沌映射麻雀优化算法，是一种基于混沌映射和麻雀行为的智能优化算法，能够有效地应用于解决复杂的优化问题。
quorum冷冻传输工作原理quorum是一种基于以太坊区块链的企业级分布式账本平台。
在传输数据时，quorum利用了冷冻传输的工作原理，以确保数据的安全性和可靠性。
冷冻传输是一种在数据传输过程中使用冷冻技术保证数据的完整性和安全性的方法。
在quorum中，冷冻传输用于确保在数据从一个节点传输到另一个节点的过程中，数据不会被篡改或泄露。
quorum使用了加密技术来保护数据的机密性。
在数据传输之前，发送方使用加密算法对数据进行加密，然后将加密后的数据传输给接收方。
接收方收到数据后，使用相同的密钥和算法对数据进行解密，从而恢复原始数据。
这样，即使在传输过程中数据被截获，攻击者也无法获得有意义的信息，因为他们没有正确的密钥来解密数据。
quorum使用了数字签名技术来验证数据的完整性和真实性。
在数据传输之前，发送方使用自己的私钥对数据进行数字签名，然后将签名和数据一起传输给接收方。
接收方使用发送方的公钥来验证签名的有效性，以确保数据没有被篡改。
如果签名验证成功，接收方可以确定数据的完整性和真实性。
如果签名验证失败，接收方将拒绝接受数据或采取其他必要的措施来确保数据的安全性。
quorum还使用了分布式一致性算法来保证数据的可靠性。
在quorum 中，多个节点共同参与数据的传输和验证过程。
当一个节点发送数据时，其他节点将验证数据的正确性和完整性。
只有当大多数节点都验证通过时，数据才会被接受并存储到区块链中。
这种分布式一致性算法可以防止单点故障和数据篡改，提高数据的可靠性和安全性。
总结起来，quorum利用冷冻传输的工作原理来确保数据的安全性和可靠性。
通过加密技术保护数据的机密性，使用数字签名技术验证数据的完整性和真实性，以及应用分布式一致性算法保证数据的可靠性，quorum为企业级分布式账本平台提供了一个安全可靠的数据传输机制。
这使得quorum在金融、供应链和物联网等领域得到广泛应用，为企业提供了高效、安全和可信赖的数据交换和合作环境。
Geometric ModelingGeometric modeling is a fundamental concept in the field of computer graphics and design. It involves the creation and manipulation of digital representations of objects and environments using geometric shapes and mathematical equations. This process is essential for various applications, including animation, virtual reality, architectural design, and manufacturing. Geometric modeling plays a crucial role in bringing creative ideas to life and enabling the visualization of complex concepts. In this article, we will explore the significance of geometric modeling from multiple perspectives, including its technical aspects, creative potential, and real-world applications. From a technical standpoint, geometric modeling relies on mathematical principles to define and represent shapes, surfaces, and volumes in a digital environment. This involves the use of algorithms to generate and manipulate geometric data, enabling the creation of intricate and realistic 3D models. The precision and accuracy of geometric modeling are essential for engineering, scientific simulations, and industrial design. Engineers and designers utilize geometric modeling software to develop prototypes, analyze structural integrity, and simulate real-world scenarios. The ability to accurately model physical objects and phenomena in a virtual space is invaluable for testing and refining concepts before they are realized in the physical world. Beyond its technical applications, geometric modeling also offers immense creative potential. Artists and animators use geometric modeling tools to sculpt, texture, and animate characters and environments for films, video games, and virtual experiences. The ability to manipulate geometric primitives and sculpt organic forms empowers creatives to bring their imaginations to life in stunning detail. Geometric modeling software provides a canvas for artistic expression, enabling artists to explore new dimensions of creativity and visual storytelling. Whether it's crafting fantastical creatures or architecting futuristic cityscapes, geometric modeling serves as a medium for boundless creativity and artistic innovation. In the realm of real-world applications, geometric modeling has a profound impact on various industries and disciplines. In architecture and urban planning, geometric modeling software is used to design and visualize buildings, landscapes, and urban developments. This enables architects and urban designers toconceptualize and communicate their ideas effectively, leading to the creation of functional and aesthetically pleasing spaces. Furthermore, geometric modelingplays a critical role in medical imaging and scientific visualization, allowing researchers and practitioners to study complex anatomical structures and visualize scientific data in meaningful ways. The ability to create accurate and detailed representations of biological and physical phenomena contributes to advancementsin healthcare, research, and education. Moreover, geometric modeling is integral to the manufacturing process, where it is used for product design, prototyping,and production. By creating digital models of components and assemblies, engineers can assess the functionality and manufacturability of their designs, leading tothe development of high-quality and efficient products. Geometric modeling also facilitates the implementation of additive manufacturing technologies, such as 3D printing, by providing the digital blueprints for creating physical objects layer by layer. This convergence of digital modeling and manufacturing technologies is revolutionizing the production landscape and enabling rapid innovation across various industries. In conclusion, geometric modeling is a multifaceteddiscipline that intersects technology, creativity, and practicality. Its technical foundations in mathematics and algorithms underpin its applications in engineering, design, and scientific research. Simultaneously, it serves as a creative platform for artists and animators to realize their visions in virtual spaces. Moreover,its real-world applications extend to diverse fields such as architecture, medicine, and manufacturing, where it contributes to innovation and progress. The significance of geometric modeling lies in its ability to bridge the digital and physical worlds, facilitating the exploration, creation, and realization of ideas and concepts. As technology continues to advance, geometric modeling will undoubtedly play an increasingly pivotal role in shaping the future of design, visualization, and manufacturing.。
a r X i v :h e p -p h /9610288v 1 8 O c t 1996NIKHEF 96-024hep-ph/9610288Quark transverse momentum in hard scattering processes1R.Jakob 1,A.Kotzinian 2,3,4,P.J.Mulders(2π)4d 4ξe i p ·ξ P,S |(2π)4d 4ξe ik ·ξ 0|ψi (ξ)|P h ,X P h ,X |1Contributed paper at the 12th International Symposium on High Energy Spin Physics,Ams-terdam,Sept.10-14,1996The important extension when transverse momenta play a role,e.g.in processes in which there are at least two hadrons in addition to the virtual photon(or W/Z) such as1-particle inclusive lepton-hadron scattering(ℓH→ℓ′hX)or Drell-Yan (AB→µ+µ−X),is the presence of transverse separations in the nonlocal matrix ing constraints coming from hermiticity,parity and time reversal in-variance the most general parametrization of the Dirac projections,Φ[Γ](x,p T)=12(2π)3e ik·ξ P,S|M,(5)Φ[iσi+γ5]=S i T h1(x,p T)+λp i T2p2T g ij T S T jM Φ[γ+γ5]∂α(x)=SαT d2p T p2TP+SαT g T(x).(8)One has the relation g2(x)=(g T−g1)(x)=d g(1)1T/dx.The factor M/P+required by Lorentz invariance,leads to a factor M/Q in the cross sections.In order to obtain the cross section for a1-particle inclusive process the distri-bution part must be combined with a fragmentation part.At leading order for the case of summing over polarizations of thefinal state hadron one encounters e.g.∆[γ−](z)=1M z h cos(φh−φS)dσLTQ4λe|S T|y(2−y) a,¯a e2a x B g(1)a1T(x B)D a1(z h),(10)where the azimuthal angles are defined with respect to the lepton scattering plane.In this expression we have used the usual scaling variables,x B =Q 2/2P ·q ,y =P ·q/P ·k and z h =P ·P h /P ·q and we have included the summation over quark flavors and the weighting with the quark chargessquared.Figure 1:The function g (1)1T(x )ob-tained from the SLAC E143data and the WW parametrization.The relation between g 2and g (1)1T allows an estimate of the latter using the SLAC E143data [4]or the Wandzura-Wilczek (WW)part of g 2.This estimate is shown in Fig.1and would lead in e p →e ′π+X to an asymmetry proportional to g (1)u 1T /f u 1which is of the order of 0.05[5].A complete analysis of lepton-hadron scatter-ing can be found in ref.[6].E.g.the functionsh ⊥1L and h ⊥1T only appear in combination witha time-reversal odd fragmentation function H ⊥1[6,7].There are several theoretical aspects that have been stepsided here,such as the inclusion of diagrams dressed with gluons.In fact a wholetower of diagrams containing matrix elements with A +gluon fields in the target matrix ele-ment also contribute at leading order,precisely summing up to a gauge link needed to renderthe nonlocal matrix element Φcolor gauge invariant.Other gluon contributions are needed to ensure electromagnetic gauge invariance at order 1/Q or they lead to perturbative QCD corrections.Summarizing,we stress the fact that inclusion of transverse momenta of quarks in the formalism of nonlocal matrix elements extends the interpretability of structure functions in terms of quark distributions.The representation in terms of nonlocal quark fields also provides a natural link to models for estimating these functions.Part of this work (R.J.and P.M.)was supported by the foundation for Fun-damental Research on Matter (FOM)and the Dutch Organization for Scientific Research (NWO).1 D.E.Soper,Phys.Rev.D 15(1977)1141;Phys.Rev.Lett.43(1979)1847;J.C.Collins and D.E.Soper,Nucl.Phys.B194(1982)445;R.L.Jaffe,Nucl.Phys.B229(1983)2052J.P.Ralston and D.E.Soper,Nucl.Phys.B 152(1979)1093 A.P.Bukhvostov,E.A.Kuraev and L.N.Lipatov,Sov.Phys.JETP 60(1984)224E143collaboration,K.Abe et al.,Phys.Rev.Lett.76(1996)5875 A.Kotzinian and P.J.Mulders,Phys.Rev.D54(1996)12296P.J.Mulders and R.D.Tangerman,Nucl.Phys.B461(1996)1977R.Jakob and P.J.Mulders,contribution at SPIN96。
量子化学波谱计算基本流程英文回答:Quantum chemistry spectroscopy calculations involve several steps to determine the electronic structure and properties of molecules. The basic workflow typically includes the following steps:1. Geometry optimization: This step involves determining the most stable structure of the molecule by minimizing its potential energy. Various optimization algorithms, such as the gradient descent method, are used to find the equilibrium geometry.2. Basis set selection: A basis set is a set of mathematical functions used to approximate the wavefunction of the molecule. The choice of basis set affects the accuracy and computational cost of the calculations. Commonly used basis sets include the Gaussian basis set and the plane wave basis set.3. Electronic structure calculation: The electronic structure of the molecule is determined by solving theSchrödinger equation. This is typically done using methods such as Hartree-Fock theory, density functional theory (DFT), or post-Hartree-Fock methods like configuration interaction (CI) or coupled cluster (CC) theory. These methods provide information about the molecular orbitals, electronic energies, and properties.4. Spectroscopic property calculation: Once the electronic structure is determined, various spectroscopic properties can be calculated. For example, the vibrational frequencies can be obtained by solving the equations of motion for the nuclei using methods like harmonic or anharmonic vibrational analysis. The rotational spectrum can be calculated using methods like rigid rotor approximation or rotational-vibrational analysis.5. Comparison with experimental data: The calculated spectroscopic properties can be compared with experimental data to validate the accuracy of the calculations. Thishelps in understanding the molecular structure and dynamics, and also in predicting and interpreting experimental spectra.中文回答：量子化学波谱计算的基本流程包括以下几个步骤：1. 几何优化，通过最小化分子的势能来确定其最稳定的结构。
a r X i v :n u c l -t h /0010067v 1 20 O c t 2000Quark-Meson Coupling Model for a NucleonS.W.Hong †,B.K.Jennings ∗†Department of Physics and Institute of Basic Science,Sungkyunkwan University,Suwon 440-746,Korea ∗TRIUMF,4004Wesbrook Mall,Vancouver,British Columbia,Canada V6T 2A3ABSTRACTWe considered the quark-meson coupling model for a nucleon.The model describes a nucleon as an MIT bag,in which quarks are coupled to the scalar and the vector mesons.A set of coupled equations for the quark and the meson fields are obtained and are solved in a self-consistent manner.We show that the mass of a dressed MIT bag interacting with σ-and ω-meson fields differs considerably from the mass of the free MIT bag.The effects of the density-dependent bag constant are investigated.The results of our calculations imply that the self-energy of the bag in the quark-meson coupling model is significant and needs to be considered in doing the calculations for nuclear matter or finite nuclei.1IntroductionFor more than a decade the success of quantum hadrodynamics 1has been rather impressive in describing the bulk properties of nuclear matter as well as the properties of finite nuclei.The model is rather simple with only a few parameters,and yet it has been successfully applied to a great number of problems for nuclear matter and nuclear structure.In this model the relevant degrees of freedom are nucleons and mesons,but the nucleons having a com-posite structure are treated as Dirac particles.Several years ago a model to remedy this problem was proposed by Guichon 2.He proposed a quark-meson coupling (QMC)model,in which quarks and mesons are explicitly dealt with.The model describes nuclear matter as non-overlapping,static,spherical MIT bags 3,4interacting through the self-consistent exchange of scalar (σ)and vector (ω)mesons in the mean-field ing this model,he investigated the direct quark degrees of freedom in nuclear matter.The model was refined1later to include the nucleon Fermi motion and the center-of-mass corrections to the bag energy5and was applied to a variety of problems[6-10].In the MIT bag model3,4the bag constant B and a phenomenological parameter Z arefixed such that the nucleon mass of939MeV is reproduced for some bag radius R.The bag constant B produces the pressure to make a bubble in the QCD vacuum.Z is to account for various corrections including the zero-point motion.In the QMC model for nuclear matter the quark-σcoupling constant(g qσ)and the quark-ωcoupling constant(g qω)are additionally ually,B and Z arefixedfirst so that the mass of the free MIT bag becomes equivalent to the nucleon mass of939MeV for a certain bag radius.We denote by B free and Z free,respectively,the bag constant B and the parameter Z for the free MIT bag.B free and Z free thus obtained are used in the QMC model calculations,and then g qσand g qωare determined to reproduce the binding energy per nucleon(B.E.=−16MeV)at the saturation density(ρ0N=0.17fm−3).However,due to the interaction between the quarks and theσ-and theω-mesons the mass of a single dressed MIT bag in free space,when calculated with B free and Z free described above,may be different from the nucleon mass of 939MeV.Such a possible deviation of the mass of a dressed bag from the value of939MeV has been neglected in previous QMC model calculations for nuclear matter.If the deviation in mass is significant,it is necessary to modify the parameters B free and Z free before implementing them in the nuclear matter calculations.In this paper we investigate this change in the nucleon mass.In Section2the QMC model for a nucleon is described.Some numerical results are presented in Section3.Section4contains a summary.2Quark-meson coupling model for a nucleonThe Lagrangian density for the MIT bag in which quarkfieldsψare coupled to theσ-andω-fields may be written asL=i2¯ψψ∆s−12m2ωωµωµ+1bag constant B(σ)asBδσ2(1−iγµnµ)ψ∆s,(3)where∆s=−n·∂(θv)is used.The left hand side of Eq.(3)gives us the equation for the quarks inside the bag,and the right hand side gives us the linear boundary condition at the bag surface.The equations forσandωµare, respectively,∂µ∂µσ+m2σσ= g qσ¯ψψ−∂B(σ)dr=− 2f(r)dr=E+(r)f(r),(7) where g(r)and f(r)are the radial parts of the upper and the lower componentsofψ,i.e.,ψ(t,r)=e−iǫq t/R g(r)−i σ·ˆr f(r) χq4π,(8)where σis the Pauli spin matrix andχq is the quark spinor.Also,E+(r)=ǫqR−g qωω0(r)−(m q−g qσσ(r))(9)3withσ(r)andω0(r)being theσ-and the time component of theω-fields.For the ground state Eqs.(9)are the equations in the radial coordinate r only.The linear boundary condition from the right hand side of Eq.(3),when rewritten by using Eq.(8),becomesf xr R (10) at the bag surface,r=R,and determines the eigenvalue x of the quarks.ǫq is then given by∂σ−g qσ(3ρs)θ(R−r)(11)and(∇2−m2ω)ω0(r)=−g qω(3ρq)θ(R−r),(12) respectively,whereρs(=¯ψψ)is the scalar density and3is explicitly multiplied by the densities(ρs andρq)here to account for the sum over3quarks.Equa-tions(11)and(12),which are nothing but the Klein-Gordon equations with source terms,may be readily solved using the Green’s function defined by the equation(∇2−m2i)G i(r,r′)=δ(r−r′)(i=σ,ω).(13) For the s-wave state G i(r,r′)may be written as11G i(r,r′)=−1m i rr′sinh(m i r<)e−m i r>.(14)Equations(6),(7),(11),and(12)form a set of coupled equations forψ,σ,and ω0,which need to be solved self-consistently.By solving these equations we can obtain the eigenvalue of the quarks and the energy of the nucleon bag.One way to calculate the energy(E N)of the nucleon is computing the energy-momentum tensor Tµνand using the relationE N= d3r T00.(15) T00may be written asT00= E q2 (∇ω0)2+(mωω0)2 +1where E q is given byE qR−ZR−ZE2N− p2c.m. ,(18) where p2c.m. = 3k=1 p2k =3(x/R)2.By calculating M N for each bag radius and minimizing M N with respect to the bag radius R,we can get the nucleon mass and the bag radius.3ResultsWefirst present some results of our calculations of the nucleon mass when we take the model parameters from Ref.[10].There are several sets of pa-rameters used in Ref.[10].Here we only consider the cases when R=0.6 fm andδ=8.In Fig.1M N is plotted as a function of the bag radius R.The solid curve represents the free MIT bag mass M freeNwithout a couplingof the quarks with the mesons;g qσ=g qω=g Bσ=0.B1/40and Z are takento be188.1MeV and2.0306,10,respectively,which produce the minimum ofM freeN at939MeV and R=0.6fm.Now we include the couplings betweenthe quarks and the mesons.We take the parameter sets used to plot Fig.1 of Ref.[10].When g qσ=0andδ=8,we have g Bσ=8.45and g qω=3.00 from Table1of Ref.[10].M N obtained with these parameters are plotted by the dashed curve in Fig. 1.M N is reduced to848MeV with R=0.694 fm.When g qσ=1.0andδ=8,and thus g Bσ=7.26and g qω=3.08from Table1of Ref.[10],we get M N as plotted by the dotted curve in Fig.1with M N=834MeV at R=0.674fm.Let us consider the case when g qσ=2.0 andδ=8.Then from Table1of Ref.[10]we have g Bσ=5.65and g qω=2.85. M N obtained with these parameters are plotted by the dash-dotted curve in Fig.1with M N=830MeV and R=0.659fm.Fig.1of Ref.[10]shows that for these three different sets of parameters the nuclear matter binding energies calculated by the QMC model are the same particularly near the saturation density.However,the present calculations show that the nucleon masses cal-culated with these parameter sets are considerably different from each other,all being far from M freeN =939MeV.The couplings induce large attractionand reduce the nucleon mass by about100MeV.Fig.1also shows that the attraction is not uniform with respect to the bag radius.There is more attrac-tion at larger bag radii,and as a result the bag radius increases significantly.5for different coupling for all calculations.curve,g qσ=1, and g Bσ=5.65.cases.Let’suse B1/40=188.1in Fig.2byquarks and theconstant,i.e.,us M N=957g qσ=2andis induced and wecurve.Whenthe attractioncurve, Now we consider the density-dependency in the bag constant using Eq.(2).We start with the case that g qσ=g qω=2and g Bσ=0,corresponding to the dash-dotted curve in Fig.2.This curve is plotted again in Fig.3by thedash-dotted curve.(M freeN is also plotted in Fig.3by the solid curve.)To seethe effects of the density-dependency of the bag constant,we take g Bσ=1, keeping g qσ=g qω= 2.The calculated M N is represented by the dashed curve.Reducing the bag constant by introducing the density-dependency6for different coupling for all calculations.g qσ=2and g qω=0.here g Bσ=0arecoupling constantis induced, from Eqs.(11) increases(nega-in enhancedfield for R=0.6fm as a function of the radial coordinate r.The dotted,dashed,and dash-dotted curves in Fig.4are obtained with the corresponding parameters used for the dotted,dashed,and dash-dotted curves in Fig.3,respectively.The figure shows that as g Bσbecomes larger theσfield increases due to the in-mass for the largersmaller mass,too.the dotted,dashed,curves,respec-only the nucleonWhen the bagessentiallyfixed asthe nucleon masswe introduceincreases as shownthe M N curveat larger bagsource functionand−g qσ3ρsDue toradii.Therefore,iffor large radii.0.8fm.σ(r)forregion,which is the significant radial region.As a result,there is more attraction at large bag radii.8−g qσ3ρs are plotted by used are g qσ=g qω=2solid and the dashed used are g qσ=g qω=20.6to1.0fm and the bag mass dueSuch self-energyinto account inchoosing the parameters for the calculation of nuclear matter properties.The density-dependent bag constant can not only change the nucleon mass but also shift the bag radius.4SummaryWe have applied the QMC model to a single nucleon.Recently the model has been often used to investigate explicit quark degrees of freedom in describing the nuclear matter.However,in the previous calculations the change in the mass of the bag due to the self-energy was ignored.Our calculations suggest that this change in the nucleon mass is not negligible,and thus the model parameters need to be modified to take this effect into consideration when they are used in nuclear matter calculations.5AcknowledgementThis work was supported by the Natural Sciences and Engineering Research Council of Canada.SWH acknowledges kind hospitality at TRIUMF and was partially supported by Sungkyun Faculty Research Fund and KOSEF Korea-Japan International Collaboration Program(986-0200-003-2).1.B.D.Serot and J.D.Walecka,Adv.Nucl.Phys.16,1(1986).2.P.A.M.Guichon,Phys.Lett.B200,235(1988).3.A.Chodos,R.L.Jaffe,K.Johnson,C.B.Thorn,and V.Weisskopf,Phys.Rev.D9,3471(1974);A.Chodos,R.L.Jaffe,K.Johnson,andC.B.Thorn,Phys.Rev.D10,2599(1974).4.A.W.Thomas,Adv.Nucl.Phys.13,1(1984).5.S.Fleck,W.Bentz,K.Shimizu,and K.Yazaki,Nucl.Phys.A510,731(1990).6.K.Saito and A.W.Thomas,Phys.Lett.B3279(1994).7.K.Saito and A.W.Thomas,Phys.Lett.B33517(1994);363157(1995);Phys.Rev.C512757(1995);522789(1995).8.A.W.Thomas,A.Michels,A.W.Schreiber,and P.A.M.Guichon,Phys.Lett.B23343(1989);K.Saito,A.Michels,and A.W.Thomas, Phys.Rev.C46R2149(1992);K.Saito and A.W.Thomas,Nucl.Phys.A574659(1994).9.H.Q.Song and R.K.Su,Phys.Lett.B358179(1995).10.X.Jin and B.K.Jennings,Phys.Lett.B37413(1996);Phys.Rev.C541427(1996).11.J.D.Jackson,Classical Electrodynamics,3rd.,(John Wiley&Sons,Inc.,New York,1999)pp.427.10。
