String Theory Demystified

by McMahon, David

• ISBN13: 9780071498708
• ISBN10: 0071498702
• Edition: 1st
• Format: Paperback
• Copyright: 2008-09-11
• Publisher: McGraw Hill

Summary

UNRAVEL the mystery of STRING THEORY Trying to understand string theory but ending up with your brain in knots? Here's your lifeline! This straightforward guide explains the fundamental principles behind this cutting-edge concept. String Theory Demystified elucidates the goal of the theory--to combine general relativity and quantum theory into a single, unified framework. You'll learn about classical strings, conformal field theory, quantization, compactification, and T duality. The book covers supersymmetry and superstrings, D-branes, the holographic principle, and cosmology. Hundreds of examples and illustrations make it easy to understand the material, and end-of-chapter quizzes and a final exam help reinforce learning. This fast and easy guide offers: Numerous figures to illustrate key concepts Sample problems with worked solutions Coverage of equations of motion, the energy-momentum tensor, and conserved currents A discussion of the Randall-Sundrum model A time-saving approach to performing better on an exam or at workSimple enough for a beginner, but challenging enough for an advanced student, String Theory Demystified is your key to comprehending this theory of everything.

Author Biography

David McMahon (Albuquerque, NM) works as a researcher in the National Laboratories on nuclear energy. He has advanced degrees in physics and applied mathematics, and has authored several titles for McGraw-Hill, most recently: Quantum Mechanics Demystified, Relativity Demystified, Linear Algebra Demystified, Signals and Systems Demystified, and Statics and Dynamics Demystified.

Table of Contents

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