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xi | |
Preface |
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xiii | |
The Authors |
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xv | |
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1 | (4) |
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1.1 Quantum Electrodynamics |
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1 | (2) |
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1.2 Units and Other Conventions |
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3 | (2) |
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Chapter 2 The Feynman Path Integral |
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5 | (12) |
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2.1 Calculation of the Transition Amplitude |
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5 | (3) |
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2.2 The Lattice Approximation |
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8 | (1) |
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9 | (1) |
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2.4 Time As A Complex Variable |
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9 | (2) |
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2.5 Statistical Mechanics |
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11 | (1) |
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12 | (5) |
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Chapter 3 Towards A Field Theory |
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17 | (20) |
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3.1 The Generating Functional |
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20 | (3) |
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3.2 The Harmonic Oscillator |
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23 | (5) |
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3.3 Free Scalar Fields: Propagator and Generating Functional |
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28 | (3) |
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3.4 Free Scalar Field: One-Particle States |
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31 | (2) |
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3.5 Creation and Destruction Operators |
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33 | (4) |
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Chapter 4 Equations of Motion, Symmetries and Ward's Identity |
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37 | (18) |
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4.1 Sum Over Paths and Operators |
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38 | (1) |
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39 | (1) |
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4.2 The Fundamental Identity |
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39 | (2) |
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41 | (5) |
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4.3.1 Equations of motion and commutation rules |
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41 | (2) |
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43 | (2) |
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4.3.3 The Hamiltonian function |
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45 | (1) |
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46 | (6) |
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4.4.1 Symmetries in field theory |
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47 | (2) |
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49 | (3) |
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4.5 The Symmetries of The Vacuum |
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52 | (3) |
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Chapter 5 The Electromagnetic Field |
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55 | (12) |
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56 | (2) |
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5.2 Generating Functional and Propagator |
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58 | (1) |
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59 | (3) |
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62 | (5) |
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67 | (18) |
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6.1 Harmonic and Fermi Oscillators |
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67 | (9) |
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6.1.1 Anticommuting variables |
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69 | (1) |
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6.1.2 Sum over paths for the two oscillators |
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70 | (4) |
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6.1.3 Gaussian integrals for commuting and anticommuting variables |
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74 | (2) |
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6.2 Quantisation of the Dirac Field |
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76 | (9) |
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79 | (1) |
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6.2.2 The spin-statistics theorem |
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79 | (2) |
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6.2.3 One-particle states of the Dirac field |
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81 | (4) |
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Chapter 7 Scattering Processes and the S-Matrix |
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85 | (14) |
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7.1 "In" States and "Out" States |
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86 | (3) |
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7.2 Scattering Amplitudes and the S-Matrix |
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89 | (1) |
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90 | (1) |
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7.4 The Lsz Reduction Formulae |
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91 | (8) |
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Chapter 8 Perturbative Green's Functions in λφ4 |
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99 | (18) |
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8.1 The Perturbative Generating Functional |
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100 | (4) |
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8.2 Feynman Rules for Green's Functions |
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104 | (6) |
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8.3 Connected Parts and Vacuum Diagrams |
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110 | (2) |
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8.4 PERTURBATIVE TWO-POINT GREEN'S FUNCTION |
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112 | (5) |
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Chapter 9 S-Matrix Feynman Diagrams in λφ4 |
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117 | (6) |
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9.1 One-Particle Irreducible Diagrams |
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117 | (3) |
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9.2 Feynman Rules for the S-Matrix Elements |
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120 | (3) |
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Chapter 10 Quantum Electrodynamics |
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123 | (16) |
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10.1 Feynman Diagrams for the Generating Functional |
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125 | (3) |
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128 | (2) |
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130 | (2) |
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10.4 Feynman Diagrams for the S-Matrix |
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132 | (4) |
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136 | (3) |
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Chapter 11 Renormalisation of Qed |
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139 | (16) |
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11.1 The Photon Propagator |
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142 | (3) |
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11.2 Renormalisation of the Charge |
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145 | (1) |
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11.3 The Electron Propagator |
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146 | (5) |
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11.3.1 The propagator to all orders |
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149 | (2) |
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151 | (2) |
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153 | (2) |
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Chapter 12 Applications of Qed |
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155 | (20) |
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12.1 Scattering In An External Field |
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155 | (3) |
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12.2 Bremsstrahlung and Infrared Divergence |
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158 | (4) |
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162 | (4) |
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166 | (3) |
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12.4.1 Calculation of the tensor Πμν(k) to one loop |
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166 | (3) |
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12.5 The Anomalous Magnetic Moment |
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169 | (6) |
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169 | (2) |
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171 | (4) |
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Chapter 13 Renormalisation Group of Qed |
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175 | (8) |
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13.1 Effective Electric Charge |
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176 | (3) |
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13.2 The Gell-Mann and Low Equation |
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179 | (1) |
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180 | (1) |
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13.4 Asymptotic Variation of the Effective Charge |
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181 | (2) |
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Chapter 14 Quantising A Non-Abelian Theory |
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183 | (12) |
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183 | (3) |
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14.2 Quarks In Quantum Chromodynamics |
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186 | (2) |
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14.3 The Faddeev-Popov Determinant |
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188 | (4) |
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192 | (3) |
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Chapter 15 The β Function In Qcd |
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195 | (10) |
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195 | (5) |
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15.2 Corrections To Quark Propagator and Vertex |
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200 | (2) |
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202 | (3) |
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Chapter 16 Unitarity and Ghosts |
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205 | (12) |
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206 | (1) |
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16.2 The Inelastic Reaction u + u → d + d |
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207 | (3) |
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210 | (2) |
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16.4 Non-Abelian Gauge Theories |
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212 | (5) |
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Chapter 17 Effective Constants At High Energy and Grand Unification |
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217 | (12) |
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17.1 The Determination Of αs |
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217 | (1) |
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17.2 The Landau Pole and the Continuum Limit |
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218 | (2) |
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17.3 Effective Constants of the Standard Theory |
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220 | (4) |
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17.4 Grand Unification and Other Hypotheses |
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224 | (5) |
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Chapter 18 Limits on the Mass of the Higgs Boson |
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229 | (10) |
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18.1 Scalar Fields In the Standard Theory |
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229 | (5) |
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18.2 Limits On the Mass of the Higgs Boson |
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234 | (5) |
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Chapter 19 The Weak Muon Anomaly |
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239 | (12) |
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240 | (4) |
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19.2 Muon Anomaly: W Exchange |
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244 | (3) |
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19.3 Z and Higgs Boson Exchange |
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247 | (1) |
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19.4 Comparison With Data |
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248 | (3) |
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Chapter 20 Effective Potential and Naturalness |
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251 | (18) |
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251 | (2) |
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20.2 Expansion Around the Classical Limit |
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253 | (4) |
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20.3 Loop Expansion of the Potential |
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257 | (1) |
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20.4 One Loop Potential in the Standard Theory |
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258 | (6) |
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20.5 Non-Naturalness of the Standard Theory |
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264 | (5) |
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Appendix A Transition Amplitude Calculation |
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269 | (2) |
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A.1 Transition Amplitude for Zero Potential |
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269 | (2) |
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Appendix B Connected Diagrams |
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271 | (4) |
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B.1 Generating Functional of Connected Diagrams |
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271 | (4) |
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Appendix C Lorentz invariance and one-particle states |
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275 | (4) |
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C.1 Renormalisation Constants |
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275 | (4) |
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Appendix D Reduction formulae |
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279 | (4) |
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D.1 Reduction Formulae for the Compton Scattering Amplitude |
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279 | (4) |
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283 | (4) |
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E.1 Integration In D Dimensions |
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283 | (2) |
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285 | (2) |
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Appendix F β(λ) and β(gt) functions |
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287 | (8) |
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F.1 Calculation of the β(λ) and β(gt) Functions |
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287 | (1) |
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287 | (6) |
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293 | (2) |
Bibliography |
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295 | (4) |
Index |
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299 | |