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Table of Wholeness Charts |
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ix | |
| Preface to Second Edition |
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x | |
| Acknowledgements for Second Edition |
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x | |
| Preface |
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xi | |
| Prerequisites |
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xv | |
| Acknowledgements |
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xv | |
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1 | (10) |
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1.0 Purpose of the
Chapter |
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1 | (1) |
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1.1 This Book's Approach to QFT |
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1 | (1) |
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1.2 Why Quantum Field Theory? |
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1 | (1) |
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1.3 How Quantum Field Theory? |
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1 | (2) |
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1.4 From Whence Creation and Destruction Operators? |
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3 | (1) |
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1.5 Overview: The Structure of Physics and QFT's Place Therein |
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3 | (2) |
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1.6 Comparison of Three Quantum Theories |
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5 | (3) |
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1.7 Major Components of QFT |
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8 | (1) |
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1.8 Points to Keep in Mind |
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8 | (1) |
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1.9 Big Picture of Our Goal |
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8 | (1) |
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1.10 Summary of the
Chapter |
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9 | (1) |
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9 | (1) |
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9 | (2) |
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11 | (28) |
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11 | (1) |
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2.1 Natural Units and Dimensions |
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11 | (4) |
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15 | (1) |
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2.3 Classical vs Quantum Plane Waves |
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16 | (1) |
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2.4 Review of Variational Methods |
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17 | (2) |
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2.5 Classical Mechanics: An Overview |
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19 | (6) |
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2.6 Schrodinger vs Heisenberg Pictures |
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25 | (4) |
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2.7 Quantum Theory: An Overview |
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29 | (2) |
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31 | (1) |
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2.9 Appendix: Understanding Contravariant and Covariant Components |
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32 | (4) |
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36 | (3) |
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39 | (142) |
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40 | (44) |
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40 | (1) |
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3.1 Relativistic Quantum Mechanics: A History Lesson |
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41 | (6) |
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3.2 The Klein-Gordon Equation in Quantum Field Theory |
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47 | (4) |
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3.3 Commutation Relations: The Crux of QFT |
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51 | (2) |
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3.4 The Hamiltonian in QFT |
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53 | (4) |
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3.5 Expectation Values and the Hamiltonian |
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57 | (1) |
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3.6 Creation and Destruction Operators |
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58 | (3) |
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3.7 Probability, Four-Currents, and Charge Density |
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61 | (2) |
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63 | (2) |
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65 | (1) |
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3.10 Characteristics of Klein-Gordon States |
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65 | (1) |
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66 | (3) |
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3.12 Harmonic Oscillators and QFT |
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69 | (1) |
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3.13 The Scalar Feynman Propagator |
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70 | (8) |
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78 | (1) |
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3.15 Appendix A: Klein-Gordon Equation from H.P. Equation of Motion |
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79 | (1) |
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3.16 Appendix B: Vacuum Quanta and Harmonic Oscillators |
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80 | (1) |
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3.17 Appendix C: Propagator Derivation Step 4 for Δ |
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81 | (1) |
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3.18 Appendix D: Enlarging the Integration Path of Fig. 3--6 |
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81 | (1) |
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82 | (2) |
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4 Spinors: Spin 1/2 Fields |
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84 | (50) |
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84 | (1) |
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4.1 Relativistic Quantum Mechanics for Spinors |
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85 | (18) |
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4.2 The Dirac Equation in Quantum Field Theory |
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103 | (1) |
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4.3 Anti-commutation Relations for Dirac Fields |
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104 | (1) |
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4.4 The Dirac Hamiltonian in QFT |
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105 | (4) |
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4.5 Expectation Values and the Dirac Hamiltonian |
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109 | (1) |
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4.6 Creation and Destruction Operators |
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109 | (2) |
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4.7 QFT Spinor Charge Operator and Four-Current |
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111 | (2) |
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4.8 Dirac Three Momentum Operator |
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113 | (1) |
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4.9 Dirac Spin Operator in QFT |
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113 | (2) |
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4.10 QFT Helicity Operator |
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115 | (1) |
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115 | (2) |
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4.12 The Spinor Feynman Propagator |
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117 | (5) |
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4.13 Appendix A. Dirac Matrices and ur, vs Relations |
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122 | (2) |
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4.14 Appendix B. Relativistic Spin: Getting to the Real Bottom of It All |
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124 | (7) |
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131 | (3) |
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134 | (28) |
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134 | (1) |
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5.1 Review of Classical Electromagnetism |
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135 | (9) |
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5.2 Relativistic Quantum Mechanics for Photons |
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144 | (3) |
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5.3 The Maxwell Equation in Quantum Field Theory |
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147 | (1) |
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5.4 Commutation Relations for Photon Fields |
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148 | (1) |
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5.5 The QFT Hamiltonian for Photons |
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149 | (1) |
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5.6 Other Photon Operators in QFT |
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149 | (1) |
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5.7 The Photon Propagator |
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150 | (1) |
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5.8 More on Quantization and Polarization |
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150 | (4) |
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5.9 Photon Spin Issues Similar to Spinors |
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154 | (1) |
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155 | (1) |
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155 | (5) |
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5.12 Appendix: Completeness Relations |
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160 | (1) |
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161 | (1) |
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6 Symmetry, Invariance, and Conservation for Free Fields |
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162 | (19) |
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162 | (1) |
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6.1 Introduction to Symmetry |
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163 | (4) |
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6.2 Symmetry in Classical Mechanics |
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167 | (4) |
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6.3 Transformations in Quantum Field Theory |
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171 | (1) |
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6.4 Lorentz Symmetry of the Lagrangian Density |
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171 | (1) |
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6.5 Other Symmetries of the Lagrangian Density: Noether's Theorem |
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172 | (5) |
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6.6 Symmetry, Gauges, and Gauge Theory |
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177 | (1) |
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178 | |
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119 | (62) |
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Part Two Interacting Fields |
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181 | (122) |
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7 Interactions: The Underlying Theory |
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182 | (32) |
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182 | (1) |
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7.1 Interactions in Relativistic Quantum Mechanics |
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183 | (3) |
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7.2 Interactions in Quantum Field Theory |
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186 | (1) |
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7.3 The Interaction Picture |
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187 | (7) |
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7.4 The S Operator and the S Matrix |
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194 | (3) |
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7.5 Finding the S Operator |
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197 | (3) |
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200 | (1) |
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7.7 Wick's Theorem Applied to Dyson Expansion |
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201 | (3) |
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7.8 Justifying Wick's Theorem |
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204 | (5) |
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7.9 Comment on Normal Ordering of the Hamiltonian Density |
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209 | (1) |
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210 | (1) |
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7.11 Appendix A: Justifying Wick's Theorem via Induction |
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210 | (2) |
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7.12 Appendix B: Operators in Exponentials and Time Ordering |
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212 | (1) |
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213 | (1) |
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8 QED: Quantum Field Interaction Theory Applied to Electromagnetism |
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214 | (40) |
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214 | (1) |
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8.1 Dyson-Wick's Expansion for QED Hamiltonian Density |
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215 | (2) |
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217 | (1) |
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217 | (3) |
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220 | (15) |
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8.5 The Shortcut Method: Feynman Rules |
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235 | (2) |
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8.6 Points to Be Aware of |
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237 | (4) |
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8.7 Including Other Charged Leptons in QED |
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241 | (1) |
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8.8 When to Add Amplitudes and When to Add Probabilities |
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242 | (1) |
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8.9 Wave Packets and Complex Sinusoids |
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243 | (1) |
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8.10 Looking Closer at Attraction and Repulsion |
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243 | (3) |
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8.11 The Degree of the Propagator Contribution to the Transition Amplitude |
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246 | (1) |
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8.12 Summary of Where We Have Been: Chaps. 7 and 8 |
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247 | (5) |
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252 | (2) |
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9 Higher Order Corrections |
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254 | (13) |
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254 | (1) |
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9.1 Higher Order Correction Terms |
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255 | (10) |
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265 | (2) |
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267 | (19) |
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267 | (1) |
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10.1 Vacuum Fluctuations: The Theory |
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267 | (3) |
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10.2 Vacuum Fluctuations and Experiment |
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270 | (2) |
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10.3 Further Considerations of Uncertainty Principle |
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272 | (2) |
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274 | (3) |
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10.5 Further Considerations |
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277 | (1) |
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277 | (1) |
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277 | (2) |
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10.8 Appendix A: Theoretical Value for Vacuum Energy Density |
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279 | (1) |
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10.9 Appendix B: Symmetry Breaking, Mass Terms, and Vacuum Pairs |
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280 | (1) |
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10.10 Appendix C: Comparison of QFT for Discrete vs Continuous Solutions |
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281 | (3) |
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10.11 Appendix D: Free Fields and "Pair Popping" Re-visited |
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284 | (1) |
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10.12 Appendix E: Considerations for Finite Volume Interactions |
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285 | (1) |
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285 | (1) |
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11 Symmetry, Invariance, and Conservation for Interacting Fields |
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286 | (17) |
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286 | (1) |
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11.1 A Helpful Modification to the Lagrangian |
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287 | (2) |
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11.2 External Symmetry for Interacting Fields |
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289 | (1) |
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11.3 Internal Symmetry and Conservation for Interactions |
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290 | (2) |
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11.4 Global vs Local Transformations and Symmetries |
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292 | (1) |
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11.5 Local Symmetry and Interaction Theory |
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293 | (4) |
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11.6 Minimal Substitution |
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297 | (1) |
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297 | (1) |
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11.8 Appendix: Showing [ Q,S] = 0 |
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298 | (2) |
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300 | (3) |
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Part Three Renormalization -- Taming Those Notorious Infinities |
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303 | (98) |
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12 Overview of Renormalization |
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304 | (18) |
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304 | (1) |
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12.1 Whence the Term "Renormalization"? |
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305 | (1) |
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12.2 A Brief Mathematical Interlude: Regularization |
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305 | (1) |
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12.3 A Renormalization Example: Bhabha Scattering |
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306 | (4) |
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12.4 Higher Order Contributions in Bhabha Scattering |
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310 | (2) |
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12.5 Same Result for Any Interaction |
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312 | (1) |
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12.6 We Also Need to Renormalize Mass |
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312 | (1) |
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12.7 The Total Renormalization Scheme |
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313 | (1) |
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12.8 Express e (k) as e (p) or Other Symbol for Energy |
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313 | (4) |
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12.9 Things You May Run Into |
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317 | (1) |
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12.10 Adiabatic Hypothesis |
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318 | (1) |
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12.11 Regularization Revisited |
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319 | (1) |
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319 | (1) |
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320 | (1) |
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321 | (1) |
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13 Renormalization Toolkit |
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322 | (17) |
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322 | (1) |
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13.1 The Three Key Integrals |
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322 | (3) |
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13.2 Relations We'll Need |
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325 | (3) |
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13.3 Ward Identities, Renormalization, and Gauge Invariance |
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328 | (2) |
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13.4 Changes in the Theory with m0 Instead of m |
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330 | (1) |
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13.5 Showing the B in Fermion Loop Equals the L in Vertex Correction |
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331 | (1) |
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13.6 Re-expressing 2nd Order Corrected Propagators, Vertex, and External Lines |
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332 | (4) |
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336 | (1) |
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13.8 Appendix: Finding Ward Identities for Compton Scattering |
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337 | (1) |
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337 | (2) |
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14 Renormalization: Putting It All Together |
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339 | (35) |
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339 | (1) |
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14.1 Renormalization Example: Compton's Scattering |
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340 | (2) |
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14.2 Renormalizing 2nd Order Divergent Amplitudes |
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342 | (9) |
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14.3 The Total Amplitude to 2nd Order |
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351 | (1) |
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14.4 Renormalization to Higher Orders: Our Approach |
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351 | (1) |
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14.5 Higher Order Renormalization Example: Compton's Scattering |
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352 | (2) |
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14.6 Renormalizing nth Order Divergent Amplitudes |
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354 | (10) |
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14.7 The Total Amplitude to nth Order |
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364 | (1) |
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14.8 Renormalization to All Orders |
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364 | (1) |
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365 | (7) |
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14.10 Appendix: Showing kμkv Bnth Term Drops Out |
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372 | (1) |
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373 | (1) |
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374 | (27) |
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374 | (1) |
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15.1 Relations We'll Need |
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375 | (4) |
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15.2 Finding Photon Self Energy Factor Using the Cut-Off Method |
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379 | (5) |
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15.3 Pauli-Villars Regularization |
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384 | (1) |
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15.4 Dimensional Regularization |
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385 | (3) |
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15.5 Comparing Various Regularization Approaches |
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388 | (1) |
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15.6 Finding Photon Self Energy Factor Using Dimensional Regularization |
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388 | (5) |
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15.7 Finding the Vertex Correction Factor Using Dimensional Regularization |
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393 | (4) |
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15.8 Finding Fermion Self Energy Factor Using Dimensional Regularization |
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397 | (1) |
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397 | (2) |
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15.10 Appendix: Additional Notes on Integrals |
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399 | (1) |
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400 | (1) |
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Part Four Application to Experiment |
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401 | (120) |
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16 Postdiction of Historical Experimental Results |
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402 | (30) |
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402 | (1) |
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16.1 Coulomb Potential in RQM |
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402 | (2) |
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16.2 Coulomb Potential in QFT |
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404 | (6) |
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16.3 Other Potentials and Boson Types |
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410 | (1) |
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16.4 Anomalous Magnetic Moment |
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411 | (16) |
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427 | (1) |
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16.6 A Note on QED Successes Over RQM |
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427 | (1) |
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428 | (2) |
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16.8 Appendix: Deriving Feynman Rules for Static, External (Potential) Field |
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430 | (1) |
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431 | (1) |
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432 | (56) |
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432 | (1) |
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432 | (13) |
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17.2 Review of Interaction Conservation Laws |
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445 | (4) |
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17.3 Another Look at Macroscopic Charged Particles Interacting |
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449 | (3) |
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17.4 Scattering in QFT: An In Depth Look |
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452 | (11) |
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17.5 Scattering in QFT: Some Examples |
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463 | (16) |
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17.6 Bremsstrahlung and Infra-red Divergences |
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479 | (3) |
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482 | (1) |
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482 | (3) |
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485 | (3) |
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487 | (1) |
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18 Path Integrals in Quantum Theories |
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488 | (22) |
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488 | (1) |
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488 | (1) |
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18.2 Defining Functional Integral |
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489 | (1) |
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18.3 The Transition Amplitude |
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490 | (2) |
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18.4 Expressing the Wave Function Peak in Terms of the Lagrangian |
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492 | (1) |
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18.5 Feynman's Path Integral Approach: The Central Idea |
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493 | (1) |
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18.6 Superimposing a Finite Number of Paths |
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494 | (3) |
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18.7 Summary of Approaches |
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497 | (1) |
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18.8 Finite Sums to Functional Integrals |
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498 | (4) |
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18.9 An Example: Free Particle |
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502 | (4) |
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18.10 QFT via Path Integrals |
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506 | (3) |
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509 | (1) |
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509 | (1) |
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509 | (1) |
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19 Looking Backward and Looking Forward: Book Summary and What's Next |
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510 | (11) |
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510 | (1) |
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511 | (8) |
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519 | (2) |
| Index |
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521 | |
