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xi | |
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xvii | |
Preface |
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xix | |
Acknowledgements |
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xxi | |
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Part I Theoretical Framework |
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1 | (146) |
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1 Decoupling and Hierarchies of Scale |
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5 | (13) |
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1.1 An Illustrative Toy Model |
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6 | (3) |
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1.1.1 Semiclassical Spectrum |
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6 | (1) |
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7 | (2) |
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1.1.3 The Low-Energy Limit |
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9 | (1) |
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1.2 The Simplicity of the Low-Energy Limit |
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9 | (7) |
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1.2.1 Low-Energy Effective Actions |
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10 | (1) |
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11 | (2) |
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1.2.3 Symmetries: Linear vs Nonlinear Realization |
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13 | (3) |
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16 | (2) |
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16 | (2) |
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18 | (33) |
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2.1 Generating Functionals -- A Review |
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18 | (8) |
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2.1.1 Connected Correlations |
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21 | (1) |
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2.1.2 The 1PI (or Quantum) Action |
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22 | (4) |
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2.2 The High-Energy/Low-Energy Split |
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26 | (6) |
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2.2.1 Projecting onto Low-Energy States |
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26 | (2) |
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2.2.2 Generators of Low-Energy Correlations |
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28 | (1) |
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29 | (3) |
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32 | (7) |
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33 | (6) |
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2.4 Dimensional Analysis and Scaling |
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39 | (5) |
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2.4.1 Dimensional Analysis |
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39 | (4) |
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43 | (1) |
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2.5 Redundant Interactions |
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44 | (4) |
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48 | (3) |
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49 | (2) |
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3 Power Counting and Matching |
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51 | (31) |
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3.1 Loops, Cutoffs and the Exact RG |
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52 | (12) |
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3.1.1 Low-Energy Amplitudes |
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53 | (1) |
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3.1.2 Power Counting Using Cutoffs |
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54 | (5) |
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3.1.3 The Exact Renormalization Group |
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59 | (4) |
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3.1.4 Rationale behind Renormalization |
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63 | (1) |
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3.2 Power Counting and Dimensional Regularization |
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64 | (12) |
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3.2.1 EFTs in Dimensional Regularization |
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65 | (3) |
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3.2.2 Matching vs Integrating Out |
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68 | (3) |
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3.2.3 Power Counting Using Dimensional Regularization |
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71 | (3) |
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3.2.4 Power Counting with Fermions |
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74 | (2) |
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76 | (3) |
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3.3.1 Low-Energy Theorems |
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76 | (1) |
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3.3.2 The Effective-Action Logic |
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77 | (2) |
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79 | (3) |
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79 | (3) |
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82 | (34) |
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4.1 Symmetries in Field Theory |
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82 | (8) |
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4.1.1 Unbroken Continuous Symmetries |
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84 | (3) |
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4.1.2 Spontaneous Symmetry Breaking |
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87 | (3) |
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4.2 Linear vs Nonlinear Realizations |
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90 | (15) |
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4.2.1 Linearly Realized Symmetries |
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91 | (2) |
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4.2.2 Nonlinearly Realized Symmetries |
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93 | (6) |
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99 | (6) |
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105 | (8) |
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105 | (3) |
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108 | (5) |
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113 | (3) |
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113 | (3) |
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116 | (10) |
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5.1 `Induced' Boundary Conditions |
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116 | (3) |
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5.2 The Low-Energy Perspective |
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119 | (3) |
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5.3 Dynamical Boundary Degrees of Freedom |
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122 | (1) |
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123 | (3) |
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124 | (2) |
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126 | (21) |
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6.1 Sample Time-Dependent Backgrounds |
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126 | (3) |
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128 | (1) |
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6.2 EFTs and Background Solutions |
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129 | (8) |
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6.2.1 Adiabatic Equivalence of EFT and Full Evolution |
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129 | (3) |
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6.2.2 Initial Data and Higher-Derivative Instabilities |
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132 | (5) |
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6.3 Fluctuations about Evolving Backgrounds |
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137 | (7) |
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6.3.1 Symmetries in an Evolving Background |
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138 | (3) |
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6.3.2 Counting Goldstone States and Currents |
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141 | (3) |
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144 | (3) |
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145 | (2) |
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Part II Relativistic Applications |
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147 | (126) |
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7 Conceptual Issues (Relativistic Systems) |
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151 | (37) |
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7.1 The Fermi Theory of Weak Interactions |
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151 | (4) |
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7.1.1 Properties of the W Boson |
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151 | (2) |
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153 | (2) |
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7.2 Quantum Electrodynamics |
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155 | (14) |
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7.2.1 Integrating Out the Electron |
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156 | (6) |
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7.2.2 E >> me and Large Logs |
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162 | (2) |
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7.2.3 Muons and the Decoupling Subtraction Scheme |
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164 | (3) |
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7.2.4 Gauge/Goldstone Equivalence Theorems |
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167 | (2) |
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7.3 Photons, Gravitons and Neutrinos |
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169 | (8) |
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7.3.1 Renormalizable Interactions |
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169 | (2) |
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7.3.2 Strength of Non-renormalizable Interactions |
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171 | (2) |
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7.3.3 Neutrino-Photon Interactions |
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173 | (4) |
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177 | (8) |
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7.4.1 Surfaces between Media |
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178 | (4) |
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182 | (3) |
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185 | (3) |
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186 | (2) |
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8 QCD and Chiral Perturbation Theory |
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188 | (24) |
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8.1 Quantum Chromodynamics |
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188 | (7) |
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188 | (2) |
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190 | (2) |
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8.1.3 Symmetries and Their Realizations |
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192 | (3) |
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8.2 Chiral Perturbation Theory |
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195 | (13) |
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8.2.1 Nonlinear Realization |
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195 | (4) |
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199 | (4) |
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203 | (2) |
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205 | (3) |
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208 | (4) |
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209 | (3) |
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9 The Standard Model as an Effective Theory |
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212 | (29) |
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9.1 Particle Content and Symmetries |
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213 | (8) |
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215 | (3) |
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9.1.2 Anomaly Cancellation |
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218 | (3) |
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9.2 Non-renormalizable Interactions |
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221 | (5) |
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9.2.1 Dimension-Five Interactions |
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222 | (2) |
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9.2.2 Dimension-Six Interactions |
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224 | (2) |
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226 | (12) |
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9.3.1 Technical and 't Hooft Naturalness |
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226 | (5) |
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9.3.2 The Electroweak Hierarchy Problem |
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231 | (5) |
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9.3.3 The Cosmological Constant Problem |
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236 | (2) |
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238 | (3) |
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239 | (2) |
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10 General Relativity as an Effective Theory |
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241 | (32) |
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10.1 Domain of Semi-Classical Gravity |
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243 | (4) |
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10.2 Time-Dependence and Cosmology |
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247 | (10) |
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10.2.1 Semiclassical Perturbation Theory |
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249 | (3) |
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10.2.2 Slow-Roll Suppression |
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252 | (5) |
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10.3 Turtles All the Way Down? |
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257 | (12) |
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257 | (7) |
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264 | (5) |
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269 | (4) |
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270 | (3) |
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Part III Nonrelativistic Applications |
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273 | (114) |
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11 Conceptual Issues (Nonrelativistic Systems) |
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277 | (19) |
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11.1 Integrating Out Antiparticles |
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277 | (3) |
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11.2 Nonrelativistic Scaling |
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280 | (4) |
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280 | (2) |
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282 | (2) |
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11.3 Coupling to Electromagnetic Fields |
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284 | (9) |
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285 | (4) |
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289 | (4) |
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293 | (3) |
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294 | (2) |
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12 Electrodynamics of Nonrelativistic Particles |
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296 | (39) |
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12.1 Schrodinger from Wilson |
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296 | (11) |
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12.1.1 Leading Electromagnetic Interactions |
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296 | (2) |
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298 | (8) |
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12.1.3 Thomson Scattering |
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306 | (1) |
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12.2 Multiple Particle Species |
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307 | (19) |
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12.2.1 Atoms and the Coulomb Potential |
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309 | (2) |
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12.2.2 Dipole Approximation |
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311 | (3) |
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314 | (4) |
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12.2.4 Particle-Antiparticle Systems |
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318 | (8) |
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326 | (6) |
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12.3.1 Polarizability and Rayleigh Scattering |
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326 | (4) |
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330 | (2) |
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332 | (3) |
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333 | (2) |
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13 First-Quantized Methods |
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335 | (52) |
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13.1 Effective Theories for Lumps |
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336 | (9) |
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13.1.1 Collective Coordinates |
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337 | (3) |
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13.1.2 Nonlinearly Realized Poincare Symmetry |
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340 | (4) |
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13.1.3 Other Localized Degrees of Freedom |
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344 | (1) |
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345 | (8) |
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13.2.1 Electromagnetic Couplings |
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346 | (2) |
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13.2.2 Gravitational Couplings |
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348 | (1) |
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13.2.3 Boundary Conditions I |
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348 | (4) |
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13.2.4 Thomson Scattering Revisited |
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352 | (1) |
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13.3 PPEFT and Central Forces |
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353 | (27) |
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13.3.1 Boundary Conditions II |
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354 | (5) |
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13.3.2 Contact Interaction |
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359 | (6) |
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13.3.3 Inverse-Square Potentials: Fall to the Centre |
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365 | (5) |
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13.3.4 Nuclear Effects in Atoms |
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370 | (10) |
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380 | (7) |
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381 | (6) |
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Part IV Many-Body Applications |
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387 | (127) |
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14 Goldstone Bosons Again |
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391 | (32) |
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391 | (12) |
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14.1.1 Antiferromagnetism |
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392 | (5) |
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397 | (4) |
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14.1.3 Physical Applications |
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401 | (2) |
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14.2 Low-Energy Superconductors |
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403 | (10) |
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14.2.1 Implications of the Goldstone Mode |
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404 | (6) |
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14.2.2 Landau-Ginzburg Theory |
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410 | (3) |
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413 | (7) |
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14.3.1 Goldstone Counting Revisited |
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413 | (2) |
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415 | (3) |
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418 | (2) |
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420 | (3) |
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421 | (2) |
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423 | (38) |
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426 | (10) |
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15.1.1 EFT Near a Fermi Surface |
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426 | (2) |
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15.1.2 Irrelevance of Fermion Self-Interactions |
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428 | (5) |
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15.1.3 Marginal Interactions |
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433 | (3) |
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15.2 Superconductivity and Fermion Pairing |
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436 | (9) |
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436 | (5) |
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15.2.2 Phonon-Coulomb Competition |
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441 | (4) |
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15.3 Quantum Hall Systems |
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445 | (12) |
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15.3.1 Hall and Ohmic Conductivity |
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445 | (3) |
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15.3.2 Integer Quantum Hall Systems |
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448 | (4) |
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15.3.3 Fractional Quantum Hall Systems |
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452 | (5) |
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457 | (4) |
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458 | (3) |
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461 | (53) |
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462 | (5) |
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16.1.1 Statistical Framework |
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463 | (2) |
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16.1.2 Evolution through Conservation |
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465 | (2) |
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467 | (5) |
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468 | (2) |
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16.2.2 Reduced Time Evolution |
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470 | (2) |
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16.3 Mean Fields and Fluctuations |
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472 | (23) |
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16.3.1 The Mean/Fluctuation Split |
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473 | (3) |
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16.3.2 Neutrinos in Matter |
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476 | (5) |
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16.3.3 Photons: Mean-Field Evolution |
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481 | (8) |
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16.3.4 Photons: Scattering and Fluctuations |
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489 | (5) |
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16.3.5 Domain of Validity of Mean-Field Theory |
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494 | (1) |
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16.4 Late Times and Perturbation Theory |
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495 | (12) |
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16.4.1 Late-Time Resummation |
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496 | (4) |
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500 | (7) |
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507 | (7) |
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508 | (6) |
Appendix A Conventions and Units |
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514 | (15) |
Appendix B Momentum Eigenstates and Scattering |
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529 | (10) |
Appendix C Quantum Field Theory: A Cartoon |
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539 | (38) |
Appendix D Further Reading |
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577 | (14) |
References |
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591 | (45) |
Index |
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636 | |