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[资源] 弦论揭秘String Theory Demystified

Preface xi
CHAPTER 1 Introduction 1
A Quick Overview of General Relativity 2
A Quick Primer on Quantum Theory 3
The Standard Model 8
Quantizing the Gravitational Field 8
Some Basic Analysis in String Theory 10
Unifi cation and Fundamental Constants 11
String Theory Overview 12
Summary 18
Quiz 18
CHAPTER 2 The Classical String I: Equations of Motion 21
The Relativistic Point Particle 22
Strings in Space-Time 28
Equations of Motion for the String 32
The Polyakov Action 36
Mathematical Aside: The Euler Characteristic 36
Light-Cone Coordinates 39
Solutions of the Wave Equation 43
Open Strings with Free Endpoints 44
Closed Strings 46
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Open Strings with Fixed Endpoints 47
Poisson Brackets 49
Quiz 49
CHAPTER 3 The Classical String II: Symmetries and
Worldsheet Currents 51
The Energy-Momentum Tensor 52
Symmetries of the Polyakov Action 53
Transforming to a Flat Worldsheet Metric 59
Conserved Currents from Poincaré Invariance 63
The Hamiltonian 67
Summary 67
Quiz 67
CHAPTER 4 String Quantization 69
Covariant Quantization 70
Light-Cone Quantization 85
Summary 87
Quiz 87
CHAPTER 5 Conformal Field Theory Part I 89
The Role of Conformal Field Theory
in String Theory 92
Wick Rotations 93
Complex Coordinates 94
Generators of Conformal Transformations 98
The Two-Dimensional Conformal Group 100
Central Extension 104
Closed String Conformal Field Theory 105
Wick Expansion 107
Operator Product Expansion 110
Summary 114
Quiz 114
CHAPTER 6 BRST Quantization 115
BRST Operators and Introductory Remarks 116
BRST-Invariant States 118
vi String Theory Demystifi ed
BRST in String Theory-CFT 120
BRST Transformations 121
No-Ghost Theorem 125
Summary 125
Quiz 126
CHAPTER 7 RNS Superstrings 127
The Superstring Action 128
Conserved Currents 133
The Energy-Momentum Tensor 136
Mode Expansions and Boundary Conditions 140
Super-Virasoro Generators 143
Canonical Quantization 144
The Super-Virasoro Algebra 145
The Open String Spectrum 147
GSO Projection 148
Critical Dimension 149
Summary 150
Quiz 150
CHAPTER 8 Compactifi cation and T-Duality 153
Compactifi cation of the 25th Dimension 153
Modifi ed Mass Spectrum 155
T-Duality for Closed Strings 159
Open Strings and T-Duality 162
D-Branes 164
Summary 165
Quiz 165
CHAPTER 9 Superstring Theory Continued 167
Superspace and Superfi elds 168
Superfi eld for Worldsheet Supersymmetry 171
Grassman Integration 173
A Manifestly Supersymmetric Action 174
The Green-Schwarz Action 175
Space-Time Supersymmetry and Strings 180
Contents vii
Light-Cone Gauge 181
Canonical Quantization 184
Summary 185
Quiz 186
CHAPTER 10 A Summary of Superstring Theory 187
A Summary of Superstring Theory 187
Superstring Theory 190
Dualities 192
Quiz 193
CHAPTER 11 Type II String Theories 195
The R and NS Sectors 195
The Spin Field 200
Type II A String Theory 201
Type II B Theory 203
The Massless Spectrum of Different Sectors 203
Summary 204
Quiz 205
CHAPTER 12 Heterotic String Theory 207
The Action for SO(32) Theory 208
Quantization of SO(32) Theory 209
The Spectrum 214
Compactifi cation and Quantized Momentum 216
Summary 219
Quiz 219
CHAPTER 13 D-Branes 221
The Space-Time Arena 223
Quantization 225
D-Branes in Superstring Theory 230
Multiple D-Branes 230
Tachyons and D-Brane Decay 235
Summary 237
Quiz 237
viii String Theory Demystifi ed
CHAPTER 14 Black Holes 239
Black Holes in General Relativity 240
Charged Black Holes 243
The Laws of Black Hole Mechanics 246
Computing the Temperature of a Black Hole 247
Entropy Calculations for Black Holes
with String Theory 249
Summary 253
Quiz 253
CHAPTER 15 The Holographic Principle and AdS/CFT
Correspondence 255
A Statement of the Holographic Principle 256
A Qualitative Description of AdS/CFT
Correspondence 257
The Holographic Principle and M-Theory 258
More Correspondence 260
Summary 262
Quiz 262
CHAPTER 16 String Theory and Cosmology 265
Einstein’s Equations 266
Infl ation 266
The Kasner Metric 268
The Randall-Sundrum Model 273
Brane Worlds and the Ekpyrotic Universe 275
Summary 277
Quiz 278
Final Exam 279
Quiz Solutions 285
Final Exam Solutions 291
References 297
Index 299

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