内容简介
Recent years have brought a revival of work on string theory, which has been a source of fascination since its origins nearly twenty years ago.There seems to be a widely perceived need for a systematic, pedagogical exposition of the present state of knowledge about string theory. We hope that this book will help to meet this need. To give a comprehensive account of such a vast topic as string theory would scarcely be possible,even in two volumes with the length to which these have grown. Indeed,we have had to omit many important subjects, while treating others only sketchily. String field theory is omitted entirely (though the subject of chapter 11 is closely related to light-cone string field theory). Conformal field theory is not developed systematically, though much of the background material needed to understand recent papers on this subject is presented in chapter 3 and elsewhere.
内页插图
目录
Preface
1 Introduction
1.1 The early days of dual models
1.1.1 The Veneziano amplitude and duality
1.1.2 High-energy behavior of the Veneziano model
1.1.3 Ramifications of the Veneziano model
1.2 Dual models of everything
1.2.1 Duality and the graviton
1.2.2 Unification in higher dimensions
1.2.3 Supersymmetry
1.3 String theory
1.3.1 The massless point particle
1.3.2 Generalization to strings
1.3.3 Constraint equations
1.4 String interactions
4.1 Splitting of strings
1.4.2 Vertex operators
1.4.3 Use of vertex operators
1.4.4 Evaluation of the scattering amplitude
1.4.5 The mass of the graviton
1.5 Other aspects of string theory
1.5.1 Gravitational Ward identities
1.5.2 Open strings
1.5.3 Internal symmetries of open strings
1.5.4 Recovery of the Veneziano amplitude
1.5.5 Comparison with QCD
1.5.6 Upitarity and gravity
1.6Conclusion
2 Free bosonic strings
2.1The classical bosonic string
2.1.1 String action and its symmetries
2.1.2 The free string in Minkowski space
2.1.3 Classical covariant gauge fixing and field equations
2.2 Quantization - old covariant approach
2.2.1 Commutation relations and mode expansions
2.2.2 Virasoro algebra and physical states
2.2.3 Vertex operators
2.3 Light-cone gauge quantization
2.3.1 Light-cone gauge and Lorentz algebra
2.3.2 Construction of transverse physical states
2.3.3 The no-ghost theorem and the spectrum-generating algebra
2.3.4 Analysis of the spectrum
2.3.5 Asymptotic formulas for level densities
2.4 Summary
3 Modern covariant quantization
3.1Covariant path-integral quantization
3.1.1 Fazideev-P0pov ghosts
3.1.2 Complex world-sheet tensor calculus
3.1.3 Quantizatlon of the ghosts3.2.1 Construction of BRST charge
3.2.2 Covariant calculation of the Virasoro anomaly
3.2.3 Virasoro, conformal and gravitational anomalies
3.2.4 Bosonization of ghost coordinates
3.3 Global aspects of the string world sheet
3.4 Strings in background fields
3.4.1 Introduction of a background spa~~e-time metric
3.4.2 Weyl invariance
3.4.3 Conformal invariance and the equations of motion
3.4.4 String-theoretic corrections to general relativity
3.4.5 Inclusion of other modes
3.4.6 The dilaton expectation value and the string coupling constant
3.5Summary
4 World-sheet supersymmetry in string theory
4.1 The classical theory
4.1.1 Global world-sheet supersymmetry
4.1.2 Superspace
4.1.3 Constraint equations
4.1.4 Boundary conditions and mode expansions
4.2 Quantization - the old covariant approach
4.2.1 Commutation relations and mode expansions
4.2.2 Super-Virasoro algebra and physical states
4.2.3 Boson-emission vertex operators
4.3 Light-cone gauge quantization
4.3.1 The light-cone gauge
4.3.2 No-ghost theorem and the spectrum-generating algebra
4.3.3 The GSO conditions
4.3.4 Locally supersymmetric form of the action
4.3.5 Superstring action and its symmetries
4.4 Modern covariant quantization
4.4.1 Faddeev-Popov ghosts
4.4.2 BRST symmetry
4.4.3 Covariant computation of the Virasoro anomaly
4.5 Extended world-sheet supersymmetry
4.5.1 The N = 2 theory
4.5.2 The N = 4 theory
4.6Summary
4.A Super Yang-Mills theories
5 Space-time supersymmetry in string theory
5.1 The classical theory
5.1.1 The superparticle
5.1.2 The supersymmetric string action
5.1.3 The local fermionic symmetry
5.1.4 Type I and type II superstrings
5.2 Quantization
5.2.1 Light-cone gauge
5.2.2 Super-Poincar
5.3.2 Closed superstrings
5.4 Remarks concerning covariant quantization
5.5 Summary
5.A Properties of SO(2n) groups
5.B The spin(8) Clifford algebra
6 Nonabelian gauge symmetry
6.1Open strings
6.1.1 The Chan-Paton method
6.1.2 Allowed gauge groups and:representations
6.2 Current algebra on the string world sheet
6.3Heterotic strings
6.3.1 The SO(32) theory
6.3.2 The Es x Es theory
6.4Toroidal compactification
6.4.1 Compactification on a circle
6.4.2 Fermionization
6.4.3 Bosonized description of the heterotic string
6.4.4 Vertex operator representations
6.4.5 Formulas for the cocycles
6.4.6 The full current Mgebra
6.4.7 The Es and spin(32)/Z2 lattices
6.4.8 The heterotic string spectrum
6.5 Summary
6.A Elements of Es
6.B Modular forms
7 Tree amplitudes
7.1 Bosonic open strings
7.1.1 The structure of tree amplitudes
7.1.2 Decoupling of ghosts
7.1.3 Cyclic symmetry
7.1.4 Examples
7.1.5 Tree-level gauge invariance
7.1.6 The twist operator
7.2 Bosonic closed strings
7.2.1 Construction of tree amplitudes
7.2.2 Examples
7.2.3 Relationship to open-string trees
7.3 Superstrings in the RNS formulation
7.3.1 Open-string tree amplitudes in the bosonic sector
7.3.2 The F1 picture
7.3.3 Examples
7.3.4 Tree amplitudes with one fermion line
7.3.5 Fermion-emission vertices
7.4 Superstrings in the supersymmetric formulation
7.4.1 Massless particle vertices
7.4.2 Open-string trees
7.4.3 Closed-string trees
7.4.4 Heterotic-string trees
7.5 Summary
7.A Coherent-state methods and correlation functions
Bibliography
Index
前言/序言
Recent years have brought a revival of work on string theory, which has been a source of fascination since its origins nearly twenty years ago.There seems to be a widely perceived need for a systematic, pedagogical exposition of the present state of knowledge about string theory. We hope that this book will help to meet this need. To give a comprehensive account of such a vast topic as string theory would scarcely be possible,even in two volumes with the length to which these have grown. Indeed,we have had to omit many important subjects, while treating others only sketchily. String field theory is omitted entirely (though the subject of chapter 11 is closely related to light-cone string field theory). Conformal field theory is not developed systematically, though much of the background material needed to understand recent papers on this subject is presented in chapter 3 and elsewhere.
《弦之律动:宇宙结构的探秘》 内容简介 本书旨在为对现代物理学前沿,特别是统一场论的构建充满好奇的读者,提供一个系统而深入的视角,探讨超越标准模型框架的全新物理图景。我们不聚焦于特定数学框架的详细推导,而是侧重于构建这些理论背后的核心物理直觉、历史演进,以及它们如何尝试解决现有理论的根本矛盾。 第一部分:物理学的黄昏与黎明——回顾与挑战 在本书的开篇,我们将追溯二十世纪物理学最伟大的成就——量子力学和广义相对论——的辉煌历程。这两大理论体系各自在微观和宏观世界取得了无可匹敌的成功。然而,它们的结合却如同水火不容。我们将详细剖析为什么在黑洞奇点或宇宙大爆炸的初始时刻,当我们试图同时描述引力与其他基本力(电磁力、弱核力、强核力)时,现有的量子场论会崩溃,产生不可消除的无穷大。 这一困境促使物理学家寻找一种全新的基本粒子描述方式。传统的点状粒子描述,在极高能量下,其相互作用的截面会失控增长,这本身就是理论失效的信号。我们探讨了粒子物理学标准模型(Standard Model)的边界:它虽然完美地描述了除引力外的所有已知现象,但它无法解释暗物质、暗能量的本质,无法统一耦合常数,更遑论将引力纳入量子的范畴。 第二部分:从点到线——维度的革命性转变 本书的核心论述建立在一个激进的假设之上:宇宙中最基本的实体不是零维的点状粒子,而是微小的、一维的、振动的“弦”。我们将深入探讨从点粒子到一维弦的转变在物理上意味着什么。 弦的引入如何解决无穷大问题?当粒子被视为一个有长度的实体时,其相互作用的“碰撞”不再是发生在零点上的尖锐接触,而是拉伸和弯曲的柔和过程。这种几何上的平滑化,使得在量子级别上处理引力相互作用时,那些令人头疼的无穷大被自然地消除或重新分配到更高维度的数学结构中。 我们不会陷入复杂的拓扑学和费曼图计算,而是侧重于理解弦的不同“振动模式”如何对应于我们观察到的不同基本粒子:电子、夸特、光子,以及至关重要的——引力子。这个概念的美妙之处在于,它提供了一种自然的方式来包含引力子(引力场的量子)与规范粒子(描述其他力的粒子)在同一个框架内。 第三部分:超越三维空间——高维度的必要性 构建一个自洽的、不含紫外灾难的量子引力理论,需要一个意想不到的代价:额外的空间维度。本书将详尽阐述为什么我们熟悉的四维时空(三维空间加一维时间)不足以维持这个理论的数学一致性。 我们将探索卡鲁扎-克莱因(Kaluza-Klein)理论的深刻见解,它首次暗示了高维度的可能性。随后,我们转向现代理论对维度的需求。这些额外的维度——通常是十维或十一维的总和——是如何隐藏起来的?我们详细介绍了“紧致化”(Compactification)的概念。想象一根极细的水管,从远处看它似乎是一维的线,但走近后会发现它有一个二维的圆形截面。同样,这些额外的空间维度被“卷曲”成极其微小的几何形状,小到无法被我们现有的低能实验观测到。 我们专注于讨论这些紧致化空间的形状对我们所观测到的低能物理学(即我们宇宙中的粒子种类、质量和力学常数)的决定性影响。不同的紧致化几何,将导致完全不同的物理定律。 第四部分:从一到多——五种理论的汇合 在引入额外维度的过程中,物理学家们发现自己面对的不是一个单一的理论,而是至少五种看起来截然不同,但内在高度关联的五维理论(Type I, Type IIA, Type IIB, 异构 I, 异构 II)。这似乎暗示着理论的不确定性。 本书将带领读者穿越“对偶性”(Duality)的迷宫。对偶性揭示了这些看似不同的理论实际上是同一个更宏大、更基础理论在不同极限或视角下的不同描述。例如,强耦合下的一个理论,可能等效于另一个理论在弱耦合下的描述。这种深刻的内在联系,是理论统一性的强大证据。 第五部分:M理论的曙光与膜世界 在对偶性的指引下,物理学家们意识到,所有这些描述似乎都指向一个更基础的、十一维的框架,通常被称为“M理论”。M理论不仅包含了五种弦理论,还将“膜”(Branes)的概念引入了核心。 弦不再是唯一的构件,它们可以扩展到更高维度,成为P-膜(P-branes)。其中,二维的膜(D-branes)扮演了至关重要的角色。我们探讨了如何将我们四维世界的粒子(如光子、电子)理解为附着在这些高维膜上的开弦的振动。而引力,则被认为是“闭弦”的振动,它们可以在所有高维空间中自由传播,解释了引力为何比其他力弱得多——因为它“泄漏”到了我们无法感知的维度中。 总结与展望 本书的目的是构建一个清晰的逻辑链条,展示理论物理学家如何从标准模型的失败中汲取教训,通过引入一维的振动实体和额外空间维度,最终汇聚到一个雄心勃勃的统一理论框架的设想中。我们不会提供精确的数学工具箱,而是专注于那些驱动这一革命性思维转变的物理概念、历史的偶然与必然,以及它对我们理解时空、物质和统一性的深刻哲学影响。这是一部关于想象力边界的探索,关于将宇宙视为一曲宏大交响乐的尝试。