內容簡介
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.
內頁插圖
目錄
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.
《弦之律動:宇宙結構的探秘》 內容簡介 本書旨在為對現代物理學前沿,特彆是統一場論的構建充滿好奇的讀者,提供一個係統而深入的視角,探討超越標準模型框架的全新物理圖景。我們不聚焦於特定數學框架的詳細推導,而是側重於構建這些理論背後的核心物理直覺、曆史演進,以及它們如何嘗試解決現有理論的根本矛盾。 第一部分:物理學的黃昏與黎明——迴顧與挑戰 在本書的開篇,我們將追溯二十世紀物理學最偉大的成就——量子力學和廣義相對論——的輝煌曆程。這兩大理論體係各自在微觀和宏觀世界取得瞭無可匹敵的成功。然而,它們的結閤卻如同水火不容。我們將詳細剖析為什麼在黑洞奇點或宇宙大爆炸的初始時刻,當我們試圖同時描述引力與其他基本力(電磁力、弱核力、強核力)時,現有的量子場論會崩潰,産生不可消除的無窮大。 這一睏境促使物理學傢尋找一種全新的基本粒子描述方式。傳統的點狀粒子描述,在極高能量下,其相互作用的截麵會失控增長,這本身就是理論失效的信號。我們探討瞭粒子物理學標準模型(Standard Model)的邊界:它雖然完美地描述瞭除引力外的所有已知現象,但它無法解釋暗物質、暗能量的本質,無法統一耦閤常數,更遑論將引力納入量子的範疇。 第二部分:從點到綫——維度的革命性轉變 本書的核心論述建立在一個激進的假設之上:宇宙中最基本的實體不是零維的點狀粒子,而是微小的、一維的、振動的“弦”。我們將深入探討從點粒子到一維弦的轉變在物理上意味著什麼。 弦的引入如何解決無窮大問題?當粒子被視為一個有長度的實體時,其相互作用的“碰撞”不再是發生在零點上的尖銳接觸,而是拉伸和彎麯的柔和過程。這種幾何上的平滑化,使得在量子級彆上處理引力相互作用時,那些令人頭疼的無窮大被自然地消除或重新分配到更高維度的數學結構中。 我們不會陷入復雜的拓撲學和費曼圖計算,而是側重於理解弦的不同“振動模式”如何對應於我們觀察到的不同基本粒子:電子、誇特、光子,以及至關重要的——引力子。這個概念的美妙之處在於,它提供瞭一種自然的方式來包含引力子(引力場的量子)與規範粒子(描述其他力的粒子)在同一個框架內。 第三部分:超越三維空間——高維度的必要性 構建一個自洽的、不含紫外災難的量子引力理論,需要一個意想不到的代價:額外的空間維度。本書將詳盡闡述為什麼我們熟悉的四維時空(三維空間加一維時間)不足以維持這個理論的數學一緻性。 我們將探索卡魯紮-剋萊因(Kaluza-Klein)理論的深刻見解,它首次暗示瞭高維度的可能性。隨後,我們轉嚮現代理論對維度的需求。這些額外的維度——通常是十維或十一維的總和——是如何隱藏起來的?我們詳細介紹瞭“緊緻化”(Compactification)的概念。想象一根極細的水管,從遠處看它似乎是一維的綫,但走近後會發現它有一個二維的圓形截麵。同樣,這些額外的空間維度被“捲麯”成極其微小的幾何形狀,小到無法被我們現有的低能實驗觀測到。 我們專注於討論這些緊緻化空間的形狀對我們所觀測到的低能物理學(即我們宇宙中的粒子種類、質量和力學常數)的決定性影響。不同的緊緻化幾何,將導緻完全不同的物理定律。 第四部分:從一到多——五種理論的匯閤 在引入額外維度的過程中,物理學傢們發現自己麵對的不是一個單一的理論,而是至少五種看起來截然不同,但內在高度關聯的五維理論(Type I, Type IIA, Type IIB, 異構 I, 異構 II)。這似乎暗示著理論的不確定性。 本書將帶領讀者穿越“對偶性”(Duality)的迷宮。對偶性揭示瞭這些看似不同的理論實際上是同一個更宏大、更基礎理論在不同極限或視角下的不同描述。例如,強耦閤下的一個理論,可能等效於另一個理論在弱耦閤下的描述。這種深刻的內在聯係,是理論統一性的強大證據。 第五部分:M理論的曙光與膜世界 在對偶性的指引下,物理學傢們意識到,所有這些描述似乎都指嚮一個更基礎的、十一維的框架,通常被稱為“M理論”。M理論不僅包含瞭五種弦理論,還將“膜”(Branes)的概念引入瞭核心。 弦不再是唯一的構件,它們可以擴展到更高維度,成為P-膜(P-branes)。其中,二維的膜(D-branes)扮演瞭至關重要的角色。我們探討瞭如何將我們四維世界的粒子(如光子、電子)理解為附著在這些高維膜上的開弦的振動。而引力,則被認為是“閉弦”的振動,它們可以在所有高維空間中自由傳播,解釋瞭引力為何比其他力弱得多——因為它“泄漏”到瞭我們無法感知的維度中。 總結與展望 本書的目的是構建一個清晰的邏輯鏈條,展示理論物理學傢如何從標準模型的失敗中汲取教訓,通過引入一維的振動實體和額外空間維度,最終匯聚到一個雄心勃勃的統一理論框架的設想中。我們不會提供精確的數學工具箱,而是專注於那些驅動這一革命性思維轉變的物理概念、曆史的偶然與必然,以及它對我們理解時空、物質和統一性的深刻哲學影響。這是一部關於想象力邊界的探索,關於將宇宙視為一麯宏大交響樂的嘗試。