超弦和M理论导论

出版时间:2010-4  出版社:世界图书出版公司  作者:加来道雄  页数:587  
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前言

Superstring theory (and its latest formulation, M-theory) has emerged as the most promising candidate for a quantum theory of all known interactions. Superstrings apparently solve a problem that has defied solution for the past50 years, namely the unification of the two great fundamental physical theories of the century, quantum field theory and general relativity. Superstring theory introduces an entirely new physical picture into theoretical physics and a new mathematics that has startled even the mathematicians. Ironically, although superstring theory is supposed to provide a unified field theory of the Universe, the theory itself often seems like a confused jumble of folklore, random rules of thumb, and intuitions. This is because the development of superstring theory has been unlike that of any other theory, such as general relativity, which began with a geometry and an action and later evolved into a quantum theory. Superstring theory, by contrast, has been evolving backward for the past 30 years. It has a bizarre history, beginning with the purely accidental discovery of the quantum theory in 1968 by G. Veneziano and M. Suzuki. Thumbing through old mathematics books, they stumbled by chance on the Beta function, written down in the last century by mathematician Leon hard Euler. To their amazement, they discovered that the Beta function satisfied almost all the stringent requirements of the scattering matrix describing particle interactions. Never in the history of physics has an important scientific discovery been made in quite this random fashion.

内容概要

 超弦和M理论是现代物理学中最有趣最活跃的研究课题之一。该问题比较困难同时也充满争议,一些人称之为“终极理论”,这是因为超弦理论有可能解决困扰人们多年的难题,即统一二十世纪最伟大的两个理论:广义相对论和量子场论。本书全面细致地讲解超弦理论和该领域的最新研究进展,内容包括四维超弦,Kac-Moody代数,Teichmuller空间和Calabi-Yau流形,M理论和D膜,对偶和BPS关系,矩阵模型等,可以作为研究生教材,同时对研究人员也有参考价值。作者首先简要介绍了点粒子理论,然后利用费曼路径积分详细讨论超弦理论。超弦研究需要很多数学工具,书中分别作了介绍,如指标定理,同调论和Kahler流形等。在第二版中,作者对内容做了整体修订,并添加了M理论的三个新章节。阅读本书需要量子力学和相对论的基本知识。  读者对象:理论物理、高能物理、场论和弦论等专业的高年级本科生、研究生和相关专业的科研人员。

作者简介

作者:(美国)加来道雄

书籍目录

Preface Acknowledgments Ⅰ First Quantization and Path Integrals 1 Path Integrals and Point Particles 1.1 Why Strings? 1.2 Historical Review of Gauge Theory 1.3 Path Integrals and Point Particles 1.4 Relativistic Point Particles 1.5 First and Second Quantization 1.6 Faddeev-Popov Quantization 1.7 Second Quantization 1.8 Harmonic Oscillators 1.9 Currents and Second Quantization 1.10 Summary References 2 Nambu-Goto Strings 2.1 Bosonic Strings 2.2 Gupta-Bleuler Quantization 2.3 Light Cone Quantization 2.4 BRST Quantization 2.5 Trees 2.6 From Path Integrals to Operators 2.7 Projective Invariance and Twists 2.8 Closed Strings 2.9 Ghost Elimination 2.100 Summary References 3 Superstrings 3.1 Supersymmetric Point Particles 3.2 Two-Dimensional Supersymmetry 3.3 Trees 3.4 Local Two-Dimensional Supersymmetry 3.5 Quantization 3.6 GSO Projection 3.7 Superstrings 3.8 Light Cone Quantization of the GS Action 3.9 Vertices and Trees 3.10 Summary References 4 Conformal Field Theory and Kac——Moody Algebras 4.1 Conformal Field Theory 4.2 Superconformal Field Theory 4.3 Spin Fields 4.4 Superconformal Ghosts 4.5 Fermion Vertex 4.6 Spinors and Trees 4.7 Kac-Moody Algebras 4.8 Supersymmetry 4.9 Summary References 5 Mulfiloops and Teichmuller Spaces 5.1 Unitarity 5.2 Single-Loop Amplitude 5.3 Harmonic Oscillators 5.4 Single-Loop Superstring Amplitudes 5.5 Closed Loops 5.6 Multiloop Amplitudes 5.7 Riemann Surfaces and Teichmiiller Spaces 5.8 Conformal Anomaly 5.9 Superstrings 5.10 Determinants and Singularities 5.11 Moduli Space and Grassmannians 5.12 Summary References Ⅱ Second Quantization and the Search for Geometry 6 Light Cone Field Theory 6.1 Why String Field Theory? 6.2 Deriving Point Particle Field Theory 6.3 Light Cone Field Theory 6.4 Interactions 6.5 Neumann Function Method 6.6 Equivalence of the Scattering Amplitudes 6.7 Four-String Interaction 6.8 Superstring Field Theory 6.9 Summary References 7 BRST Field Theory 7.1 Covariant String Field Theory 7.2 BRST Field Theory 7.3 Gauge Fixing 7.4 Interactions 7.5 Witten's String Field Theory 7.6 Proof of Equivalence 7.7 Closed Strings and Superstrings 7.8 Summary References Ⅲ Phenomenology and Model Building 8 Anomalies and the Atiyah-Singer Theorem 8.1 Beyond GUT Phenomenology 8.2 Anomalies and Feynman Diagrams 8.3 Anomalies in the Functional Formalism 8.4 Anomalies and Characteristic Classes 8.5 Dirac Index 8.6 Gravitational and Gauge Anomalies 8.7 Anomaly Cancellation in Strings 8.8 Summary References 9 Heterotic Strings and Compactification 9.1 Compactification 9.2 The Heterotic String 9.3 Spectrum 9.4 Covariant and Fermionic Formulations 9.5 Trees 9.6 Single-Loop Amplitude 9.7 Es and Kac——Moody Algebras 9.8 Lorentzian Lattices 9.9 Summary References 10 Calabi——Yau Spaces and Orbifolds 10.1 Calabi-Yau Spaces 10.2 Review of de Rahm Cohomology 10.3 Cohomology and Homology 10.4 K/ihler Manifolds 10.5 Embedding the Spin Connection 10.6 Fermion Generations 10.7 Wilson Lines 10.8 Orbifoids 10.9 Four-Dimensional Superstrings 10.10 Summary References Ⅳ M-Theory 11 M-Theory and Duality 11.1 Introduction 11.2 Duality in Physics 11.3 Why Five String Theories? 11.4 T-Duality 11.5 S-Duality 11.5.1 Type IIA Theory 11.5.2 Type IIB Theory 11.5.3 M-Theory and Type IIB Theory 11.5.4 E8 E8 Heterotic String 11.5.5 Type I Strings 11.6 Summary References 12 Compactifications and BPS States 12.1 BPS States 12.2 Supersymmetry and P-Branes 12.3 Compactification 12.4 Example: D = 6 12.4.1 D = 6, N = (2, 2) Theory 12.4.2 D = 6, N = (1, 1) Theories 12.4.3 M-Theory in D = 7 12.5 Example:D=4, N=2 and D=6, N=1 12.6 Symmetry Enhancement and Tensionless Strings 12.7 F-Theory 12.8 Example: D = 4 12.9 Summary References 13 Solitons, D-Branes, and Black Holes 13.1 Solitons 13.2 Supermembrane Actions 13.3 Five-Brahe Action 13.4 D-Branes 13.5 D-Brane Actions 13.6 M(atrix) Models and Membranes 13.7 Black Holes 13.8 Summary 13.9 Conclusion References Appendix A.1 A Brief Introduction to Group Theory A.2 A Brief Introduction to General Relativity A.3 A Brief Introduction to the Theory of Forms A.4 A Brief Introduction to Supersymmetry A.5 A Brief Introduction to Supergravity A.6 Notation References Index

章节摘录

插图:(1) Because we are dealing with a first quantized theory, we have to take the sum over all interacting topologies that are swept out by the string. For the Nambu——Goto string, the precise nature of these topologies is ambiguous and must be specified by hand. However, for the Polyakov form of the action, which contains an independent metric tensor, we can eliminate most of this ambiguity by specifying that we sum over all conformally and modular in equivalent configurations. (These terms will be defined later.) This will become a powerful constraint once we start to derive loops and will determine the function measure uniquely. The measure and the topologies in the Nambu-Goto action, however, are not well defined.  (We must point out, however, that this rule of integrating over in equivalent surfaces does not automatically satisfy unitarity. This still must be checked by hand.)(2) The gauge fixing of weyl invariance for the Polyakov action, although trivial classically, poses problems when we make the transition to quantum mechanics. An anomaly appears when we carefully begin the quantization process. In fact, this conformal anomaly will disappear only in 26dimensions.

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用户评论 (总计16条)

 
 

  •     可以开心的领略一下超弦的魅力了
  •     这本书需要一定的物理知识和很高的英语水平,不过还是很不错的
  •     这本书很专业,内容充实,如果英文水平不够,建议不要购买~
  •     同学推荐的,好吧,在借助牛津大哥慢慢看。。。希望好理解一点,我觉得这本书还是少点公式吧。。。
  •     东西很好,便宜,内容比较全,很喜欢。
  •     全英文,对我学习帮助太大了,赞!
  •     全英文的,的确是挑战。当提高英语水平了
  •     帮朋友买的,很不错,印刷很正,纸质很好,而且快递速度也很满意!
  •     至少讲得很仔细,对于初学者很有帮助
  •     全英文的要做好准备。刚翻开的时候我就看到了to my parents然后整个空白,我以为是自己要写给父母的话
  •     经典书籍 没得说
  •     太理论化了。 看不懂。
  •     可惜了。
  •     kaku写科普还是不错的,写教科书只能说一般了,其实学弦论,还是得看polchinsky的两卷本啊。
  •     对量子力学,微分几何,群论等有所了解才能学习此书,也许超弦理论会成为明日黄花,但它在人类探索宇宙奥秘的进程中应该会留下光辉的一笔.
  •     Kaku的作品,还在欣赏之中
 

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