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弦论揭秘String Theory Demystified
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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 For more information about this title, click here 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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