物理群论专题 (Group Theory and Physics)(Sidney Coleman & Shlomo Sternberg & Wu-Ki Tun Sidney ColemanShlomo SternbergWu-Ki TungMildred S· Dresselhaus等
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- 10 11 月, 2022
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原名: Group Theory and Physics
作者: 图书分类: 教育/科技 资源格式: PDF 版本: 影印版 出版社: Cambridge University Press 书号: 0-521-31827-0 发行时间: 1988年 地区: 语言: 简介: 此为入门教材，并且附上课后习题答案。看完此书才能向高阶群论进军！作者是2005年全球理论物理排名60的 Wu-Ki Tung先生，可惜他在2009年永远的离开了我们。向他老人家永远表示敬意！ 内容简介： An introductory text book for graduates and advanced undergraduates on group representation theory. It emphasizes group theory’s role as the mathematical framework for describing symmetry properties of classical and quantum mechanical systems. Familiarity with basic group concepts and techniques is invaluable in the education of a modern-day physicist. This book emphasizes general features and methods which demonstrate the power of the group-theoretical approach in exposing the systematics of physical systems with associated symmetry. Particular attention is given to pedagogy. In developing the theory, clarity in presenting the main ideas and consequences is given the same priority as comprehensiveness and strict rigor. To preserve the integrity of the mathematics, enough technical information is included in the appendices to make the book almost self-contained. 作者介绍： Wu-Ki Tung, born in Kunming, China (1939), died on Mar 30, 2009 in Seattle, Washington. He was educated at National Taiwan University and received his Ph.D. at Yale University in 1966. Wu-Ki Tung was Professor Emeritus at Michigan State University (MSU), and Affiliated Professor at University of Washington. He was a theoretical physicist, whose main interest was the study of phenomenological aspects of high energy particle physics, particularly in the field of Quantum Chromodynamics (QCD) and, more specifically, of parton distributions in hadrons. Parton distribution functions are among the standard inputs needed to compare theoretical calculations to experiments like Fermilab Tevatron and the CERN Large Hadron Collider (LHC). Wu-Ki Tung was the founder of The Coordinated Theoretical-Experimental Project on Quantum Chromodynamics Collaboration (CTEQ). He led the CTEQ global QCD analysis group to determine parton distribution functions from high energy scattering experiments of different types. Wu-Ki Tung’s group at MSU recognized the importance of developing a systematic error analysis for the global analysis, which has now been widely used in various experimental and theoretical analyses. Wu-Ki Tung was a founding member of Overseas Chinese Physics Association (OCPA) and had been actively involved in its development and activities ever since. He was also the author of an influential book Group Theory in Physics, which is used all over the world. 内容截图： 目录： 1.Basic Group Theory 此书和上一本一样，为入门教材，至少要看懂九成才可进入下一个阶段。这本书的实例很多，读起来的感觉和上面那本差不多，物理学专业的朋友应该会感到很亲切。作者为哈佛大学教授。 内容简介： Group theory is one of the great achievements of 19th century mathematics. It emerged as a unifying idea drawing on four different sources: number theory, the theory of equations, geometry, and crystallography. The early motivation from number theory stemmed from the work of Euler, Legendre and Gauss on power residues. In the theory of equations, the study of various permutation groups became increasingly important through the work of Lagrange, Ruffini, Gauss, Abel, Cauchy, and especially Galois. The discovery of new types of geometries-including non-Euclidean, affine, projective etc.-led, eventually, to the famous Erlangen program of Klein, which proposed that the true study of any geometry lies in an analysis of its group of motions. In crystallography, the possible symmetries of the internal structure of a crystal were enumerated long before there was any possibility of its physical determination (by X-ray analysis). 作者介绍： Shlomo Zvi Sternberg is a leading mathematician, known for his work in geometry, particularly symplectic geometry and the differential geometry of G-structures. Sternberg earned his Ph.D. in 1957 from Johns Hopkins University, where he wrote a dissertation on transformations under Aurel Wintner. He was a Guggenheim Fellow at Harvard University in 1974. One of his best known Ph.D. students is Victor Guillemin (1962), who has also become a leader in symplectic geometry. Sternberg has written several textbooks for undergraduate students as well as a number of monographs, some of which have been republished after several decades, an unusual distinction which indicates their importance in the field. Following the publication of The Bible Code by journalist Michael Drosnin, which was based in part upon a paper by Rips et al. which appeared in Statistical Science, Sternberg joined many other prominent mathematicians in debunking the notion that Drosnin’s controversial claims are well founded in mathematics. 目录： Preface 内容截图： 警告！！！身体弱小者、长期失眠者、意志不坚定者、患有心脏病或高血压者、喜欢网游者、无群论基础者、无量子力学基础者、无粒子物理基础者请慎下此书。本书作者为没有桂冠的“诺贝尔奖获得者”—— 哈佛大学教授Sidney Coleman。这本书是他在哈佛大学的讲义，并且第1页和第2页遗失了（有的朋友可以补充），所以没有群论基础的同学会看得云里雾里（有基础的同学都看到云里雾里）。他是诺贝尔奖得主David Politzer的论文指导老师，并且本来他也应该得奖的，可是他把自己的名字删掉了。。。学完上面两本书的同学，可以尝试看看这本神作，它绝对谋杀你的脑细胞并且让你的自信心极其低落。看这本书一定要看懂，本人也没看懂；有的时候以为自己懂了，实际上一点都没学会。不过看了两三遍之后，你的收获会很多。 内容简介： This 400-page book contains eight lectures of varying length (some are quite long). The first two are not very useful, but the remainder of the book is wonderful. It covers topics like scale invariance, Callan-Symanzik (RG) equations, renormalization theory (Hepp’s theorem), spontaneously broken symmetries, classical and quantum solitons, instantons (in QM and in gauge theories), and 1/N expansion. These are all useful topics and must be understood by those in the field, and yet not all of them are covered by ordinary quantum field theory books like Peskin & Schroeder. The style is very friendly and readable and includes a lot of endnotes, appendices, and references. This book does not "read" like Peskin/Schroeder or Weinberg or Itzykson/Zuber; those books don’t read. This one does. The equations are easy to follow and this book showcases the strength of Coleman’s pedagogical style. In fact I can vouch that the tone and content of these lectures serves as a close substitue for Coleman’s lectures themselves. The topics were all basically developed in the 1970s, and were themselves all quite hot research areas before supersymmetry and string theory revolutionized high-energy physics. However, the majority of this book is not an anachronism — the renormalization group, spontaneously broken symmetries, solitons, instantons, and 1/N expansion all pervade modern physics. 作者介绍： 2004年度的诺贝尔物理学奖授予了David J. Gross, H. David Politzer以及Frank Wilczek。但实际上这一年的诺贝尔奖应该授予四个人。 1973年，哈佛物理系的Sidney Coleman给自己的研究生David Politzer一个习题，让他用重整化群（Renormalization Group）计算非阿贝尔规范场（Non-Abelian Gauge Field Theory）的耦合常数（Coupling Constant）随动量的跑动（Running）性质，与此同时，普林斯顿物理系的David Gross也给了自己的研究生Frank Wilczek同样的习题。此时Coleman正在普林斯顿访问，知道Gross这一组也在做同样的计算，当Politzer把计算结果告诉Coleman的时候，Gross和Wilczek也得到了结果，但是两人的结果相差一个符号，于是各自拿回去检查。Politzer在哈佛到处找人帮他检查计算，最终没有发现有错误；而Wilczek发现自己的计算有个错误，而修正了错误后就得到了和Politzer相同的结果：当两个参与强作用的粒子（比如夸克）靠的很近时，其耦合强度变得非常小，而当两个粒子远离时，耦合强度变得非常大，夸克被禁闭了。这就是所谓的“渐进自由”（Asymptotic Freedom）——当两个粒子渐渐靠近时就变得自由了——此时耦合常数是一个小量，可以做微扰展开，物理学家们历史上第一次能够计算强相互作用了。并扫除了之前对于场论不信任的态度，开创了规范场论三十年来在理论物理中占据主要地位的时代。 本来这个贡献是四个人的。但Coleman当时认为这个计算不过是个习题，就没有在文章上署上自己的名字，Politzer是独立署名发表的文章，而Gross和Wilczek是联合署名发表的文章，于是发现渐进自由的荣誉就只记在了Gross、Wilczek和Politzer三人名下。这对诺贝尔奖的评选是件好事，因为按惯列得奖人不能超过三位。然而Coleman为Politzer指出了方向，可谓功不可没。 Coleman于本月18日逝世，以下是哈佛大学为其发的讣告，概括了其一生： Sidney Coleman是二十世纪下半叶理论物理中的重要人物。他在复苏和理解量子场论（Quantum Field Theory）——这是统一了量子力学（Quantum Mechanics）和狭义相对论（Special Relativity）的理论框架——方面扮演了重要的角色。他的一位获得诺贝尔物理奖的同事Steven Weinberg说过一句饱含深情并被人们广为传颂的话：“Sidney是理论物理学家中的理论物理学家。他对实验数据的关心远远比不上他对理论的深入理解。我可以说我从Sidney那里学到的东西比从任何其他人身上学到的都多。” Sidney通过他从60年代到80年代做出的工作向人们揭示了量子场理论这座宏伟大厦的深刻内涵。他的观点具有巨大的影响力，并一直作为现代理论发展的核心而被传承到了今天。他参与完成的Coleman-Mandula定理严格地限制了场论中所能具有的时空对称性；对于这个深刻理论的发展导致了超对称（Supersymmetry）的出现，这是目前所知的对于Einstein确立的时空对称性的唯一可能扩展；这一对称性在即将到来的粒子加速器上可能产生的后果正是人们目前正在努力寻找的。他深刻地理解规范理论的重要性，并阐明了重整化；这两样是我们对于场论现代理解的两个关键支柱。他对于理解强相互作用（Strong Ineraction）和所谓渐近自由给予了很大的支持，正是这一点使得他当时的研究生David Politzer能够与David Gross以及Frank Wilczek分享2004年的诺贝尔物理学奖。 此外，他还发现并推广了对偶性（Daulity）——看起来非常不一样的经典理论却可以准确地描述量子水平的一些物理现象——这一深刻的思想；这一思想成为从90年代开始的超弦（Superstring）革命的中心主题，并一直持续至今。他同时还引领了对于量子场论中虚真空隧穿（False Vacuum Tunneling）效应的研究，和这种微妙效应是如何被宇宙学改变的，从而导致了宇宙膨胀加速这一重要现象的发现，这方面的工作人们从来没有中断过，并一直持续至今。 除了作为一位研究者所具有的聪明才智外，Sidney还是一位非常出色的物理学教师。他的讲课非常清晰而富有洞察力并因此吸引了许多聪明的头脑，成为一个传奇。整整一代理论物理学家是在他的指导下步入理论物理研究领域的，他对于理论物理的独到见解也必将传承给下一代。 下一篇: 宇宙飞弹 (宇宙飞弹:天体物理学中的高能粒子)文字版 罗杰·柯莱布鲁斯·道森
Springer
2.Group Representations
3.General Properties of Irreducible Vectors and Operators
4.Representations of the Symmetric Groups
5.One-Dimensional Continuous Groups
6.Rotations in Three-Dimensional Space — The Group SO(3)
7.The Group SU(2) and More About SO(3)
8.Euclidean Groups in Two- and Three-Dimensional Space
9.The Lorentz and Poincaré Groups, and Space-Time Symmetries
10.Space Inversion Invariance
11.Time Reversal Invariance
12.Finite-Dimensional Representations of the Classical Groups
1 Basic definitions and examples
2 Representation theory of finite groups
3 Molecular vibrations and homogeneous vector bundles
4 Compact groups and Lie groups
5 The irreducible representations of SU n
Appendix A The Bravais lattices and the arithmetical crystal classes
Further reading
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