| Preface to the Dover Edition |
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xix | |
| Preface |
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xxi | |
| General References |
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xxiii | |
| Errata |
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xxv | |
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1 | (44) |
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Principle of Least Action |
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1 | (18) |
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1 | (6) |
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Lagrange and Hamilton's equations |
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Relativistic point particle |
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Canonical transformations |
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Electromagnetic Field as an Infinite Dynamical System |
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7 | (6) |
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Electromagnetic Interaction of a Point Particle |
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13 | (6) |
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Bargmann-Michel-Telegdi equation |
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Interaction with a plane wave |
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Symmetries and Conservation Laws |
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19 | (13) |
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19 | (3) |
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Time translation and energy conservation |
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Momentum and angular momentum |
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22 | (6) |
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Electromagnetic symmetric tensor |
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Generalized angular momentum |
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28 | (4) |
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Infinitesimal transformations |
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Lie algebra with Poisson brackets |
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Propagation and Radiation |
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32 | (13) |
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32 | (4) |
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Retarded and advanced Green functions |
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36 | (9) |
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Lienard-Wiechert potentials |
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Larmor's formula for the radiated power |
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45 | (60) |
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Toward a Relativistic Wave Equation |
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45 | (10) |
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Quantum Mechanics and Relativity |
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45 | (3) |
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48 | (3) |
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Conserved current with positive density |
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51 | (4) |
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55 | (17) |
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Plane Wave Solutions and Projectors |
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55 | (5) |
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Positive and negative energy solutions |
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Projectors on states with definite momentum and polarization |
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60 | (4) |
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Zitterbewegung and Klein's paradox |
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64 | (5) |
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Nonrelativistic limit and Pauli equation |
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Solutions in a constant magnetic field and in an electromagnetic plane wave |
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Foldy-Wouthuysen Transformation |
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69 | (3) |
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72 | (12) |
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Nonrelativistic Versus Relativistic Spectrum |
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72 | (2) |
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Predictions of the Klein-Gordon equation |
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74 | (10) |
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Relativistic wave functions |
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Hyperfine splitting and radiative effects |
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Hole Theory and Charge Conjugation |
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84 | (5) |
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Reinterpretation of Negative Energy Solutions |
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84 | (1) |
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85 | (2) |
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Charge conjugation operator and invariance of the Dirac equation |
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87 | (2) |
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89 | (16) |
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89 | (4) |
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Retarded and Feynman propagator from the hole theory point of view |
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Propagation in an Arbitrary External Electromagnetic Field |
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93 | (1) |
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Perturbation expansion of the propagators in an external field |
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Application to the Coulomb Scattering |
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94 | (6) |
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Classical Rutherford scattering |
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Fock-Schwinger Proper Time Method |
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100 | (5) |
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Propagation in a constant uniform field or a plane wave field |
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QUANTIZATION---FREE FIELDS |
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105 | (58) |
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105 | (22) |
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107 | (7) |
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Conjugate momenta and quantization |
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114 | (6) |
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States with fixed number of particles |
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120 | (3) |
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Particles and antiparticles |
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123 | (1) |
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Feynman's propagator recovered |
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Thermodynamic Equilibrium |
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124 | (3) |
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Bose-Einstein distribution |
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Propagators at finite temperature |
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Quantized Radiation Field |
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127 | (15) |
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127 | (6) |
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Gupta-Bleuler quantization |
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133 | (1) |
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Generalization to arbitrary λ |
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134 | (4) |
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Proca and Stueckelberg equations |
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Upper limit on the photon mass using the constant field method |
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138 | (4) |
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Dirac Field and Exclusion Principle |
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142 | (9) |
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143 | (3) |
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Dirac field quantization and positivity of the energy |
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146 | (3) |
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Antisymmetric states and Fermi-Dirac statistics |
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Relation between Spin and Statistics---Propagator |
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149 | (2) |
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The connection between spin and statistics as implied by local quantum theory |
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151 | (12) |
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151 | (1) |
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152 | (2) |
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154 | (2) |
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156 | (7) |
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Transformation properties of quadratic forms |
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Fierz reshuffling theorem |
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INTERACTION WITH AN EXTERNAL FIELD |
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163 | (35) |
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Quantized Electromagnetic Field Interacting with a Classical Source |
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163 | (17) |
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163 | (7) |
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Emitted Energy and the Infrared Catastrophe |
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170 | (4) |
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Finite energy versus infinite photon number |
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Induced Absorption and Emission |
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174 | (2) |
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S Matrix and Evolution Operator |
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176 | (4) |
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Interaction representation |
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General form of the S matrix |
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180 | (5) |
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180 | (2) |
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Wick's identities from a generating functional |
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182 | (3) |
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Grassmann algebra formalism |
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185 | (1) |
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Quantized Dirac Field Interacting with a Classical Potential |
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185 | (13) |
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185 | (6) |
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Gauge invariance and unitarity |
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Emission Rate to Lowest Order |
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191 | (2) |
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Pair Creation in a Constant Uniform Electric Field |
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193 | (2) |
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Nonperturbative tunneling effect |
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The Euler-Heisenberg Effective Lagrangian |
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195 | (3) |
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Effective action for a slowly varying field |
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198 | (63) |
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S Matrix and Asymptotic Theory |
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198 | (26) |
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199 | (3) |
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202 | (3) |
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Kallen-Lehmann representation for the vacuum expectation value of field commutators |
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205 | (3) |
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Lehmann-Symanzik-Zimmermann formalism |
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208 | (3) |
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211 | (2) |
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213 | (4) |
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217 | (7) |
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Current conservation and covariant time-ordered product |
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224 | (17) |
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224 | (6) |
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The Klein-Nishina relativistic formula |
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230 | (3) |
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233 | (5) |
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Singlet and triplet lifetimes to lowest order |
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238 | (3) |
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The Bethe-Heitler cross section for photoemission in the nuclear Coulomb field |
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241 | (20) |
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Unitarity and Partial Wave Decomposition |
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241 | (4) |
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Jacob and Wick partial wave expansion |
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Causality and Analyticity |
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245 | (4) |
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Support properties in configuration and momentum space |
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The Jost-Lehmann-Dyson Representation |
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249 | (1) |
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Forward Dispersion Relations |
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250 | (5) |
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Application to pion-nucleon scattering |
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Determination of the effective pion-nucleon coupling |
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Momentum Transfer Analyticity |
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255 | (6) |
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Small and large Lehmann ellipses |
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261 | (57) |
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Interaction Representation and Feynman Rules |
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261 | (26) |
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Self-Interacting Scalar Field |
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262 | (9) |
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Perturbative series in the interaction picture |
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Feynman rules in configuration and momentum space |
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Feynman Rules for Spinor Electrodynamics |
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271 | (5) |
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Electron-Electron and Electron-Positron Scattering |
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276 | (6) |
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Moller's and Bhabha's formulas |
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282 | (5) |
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Derivation of covariant perturbation rules and computation of elementary processes in scalar electrodynamics |
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287 | (14) |
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287 | (2) |
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Counting the number of loops in terms of powers of Planck's constant |
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Truncated and Proper Diagrams |
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289 | (5) |
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Topological and algebraic definitions |
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Parametric Representation |
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294 | (5) |
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General expression of Feynman integrals in terms of α parameters |
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Euclidean Green Functions |
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299 | (2) |
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The Wick rotation performed term by term in the perturbation expansion |
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301 | (17) |
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302 | (3) |
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305 | (3) |
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Normal and anomalous thresholds |
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Real Singularities of Simple Diagrams |
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308 | (5) |
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One-loop bubble, vertex, and box diagrams |
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The Mandelstam representation |
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Physical-Region Singularities. Cutkosky Rules |
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313 | (5) |
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318 | (54) |
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318 | (29) |
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319 | (10) |
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Vacuum polarization tensor |
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Gauge-invariant regularization |
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329 | (6) |
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Gauge-dependence and infrared problems of the electron self-energy |
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335 | (8) |
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343 | (4) |
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Counterterms and bare lagrangian |
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Radiative Corrections to the Interaction with an External Field |
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347 | (8) |
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Effective Interaction and Anomalous Magnetic Moment |
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347 | (2) |
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Radiative Corrections to Coulomb Scattering |
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349 | (3) |
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The α3 corrections to Mott's formula |
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352 | (2) |
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Finite Inclusive Cross Section |
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354 | (1) |
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355 | (17) |
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355 | (3) |
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Low- and high-energy behavior |
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Explicit expression in the zero frequency limit |
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358 | (7) |
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Radiative corrections to bound-states energy levels and computation of the Lamb shift to leading α(Zα)4 order |
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Van der Waals Forces at Large Distances |
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365 | (7) |
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Computation of the coefficient of the r-7 law in terms of static susceptibilities |
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372 | (53) |
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Regularization and Power Counting |
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372 | (13) |
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372 | (2) |
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374 | (5) |
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A review of the various procedures |
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379 | (3) |
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Superficial degree of divergence |
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Renormalizable and nonrenormalizable interactions |
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382 | (3) |
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385 | (17) |
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Normalization Conditions and Structure of the Counterterms |
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385 | (4) |
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The importance of the normalization conditions and their arbitrariness |
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Multiplicative character of the renormalization operation |
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Bogoliubov's Recursion Formula |
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389 | (3) |
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Zimmermann's Explicit Solution |
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392 | (2) |
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Renormalization in Parametric Space |
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394 | (3) |
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Form of Zimmermann's operation in parametric space |
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Indications on the Bogoliubov-Parasiuk-Hepp convergence theorem |
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397 | (2) |
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399 | (3) |
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Multiplicative renormalization in matrix form |
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Zero-Mass Limit, Asymptotic Behavior, and Weinberg's Theorem |
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402 | (5) |
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402 | (3) |
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Kinoshita-Lee-Nauenberg theorem |
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Ultraviolet Behavior and Weinberg's Theorem |
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405 | (2) |
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The Case of Quantum Electrodynamics |
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407 | (18) |
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Formal Derivation of the Ward-Takahashi Identities |
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407 | (4) |
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Pauli-Villars Regularization to All Orders |
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411 | (2) |
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413 | (2) |
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Two-Loop Vacuum Polarization |
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415 | (10) |
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An illustrative computation carried out in massless quantum electrodynamics, using dimensional regularization |
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425 | (50) |
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425 | (18) |
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The Role of the Classical Action in Quantum Mechanics |
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425 | (10) |
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Matrix element of the time evolution operator |
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Path integral over classical trajectories |
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Harmonic oscillator and evolution under the action of an external force |
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Trajectories in the Bargmann-Fock Space |
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435 | (4) |
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Hilbert space of analytic functions |
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Analytic kernel of an operator |
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Application to path integrals |
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439 | (4) |
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Derivatives and integrals |
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443 | (13) |
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S Matrix and Green Functions in Terms of Path Integrals |
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443 | (5) |
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The generating functional as a path integral |
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Effective Action and Steepest-Descent Method |
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448 | (8) |
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Perturbation theory as the semiclassical expansion around zero classical field |
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Explicit computation up to order h2 |
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456 | (7) |
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456 | (5) |
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Canonical structure of constrained systems |
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Quantization in terms of the original variables |
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The Electromagnetic Field as an Example |
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461 | (2) |
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Large Orders in Perturbation Theory |
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463 | (12) |
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463 | (4) |
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Divergence of perturbation theory |
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467 | (8) |
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Classical solutions of finite action |
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Fluctuations around a degenerate extremum |
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The Bender and Wu expression for large orders of the ground-state energy |
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INTEGRAL EQUATIONS AND BOUND-STATE PROBLEMS |
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475 | (34) |
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The Dyson-Schwinger Equations |
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475 | (6) |
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476 | (5) |
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Functional methods and integral equations |
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481 | (1) |
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Relativistic Bound States |
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481 | (12) |
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Homogeneous Bethe-Salpeter Equation |
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482 | (3) |
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Derivation of the equation |
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Normalization of the solutions |
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485 | (2) |
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Stability conditions and rotation to euclidean variables |
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Scalar Massless Exchange in the Ladder Approximation |
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487 | (6) |
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Conformal transformations |
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One-dimensional reduction |
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Hyperfine Splitting in Positronium |
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493 | (16) |
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495 | (5) |
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Instantaneous approximation |
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Salpeter's perturbation theory |
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500 | (9) |
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The Karplus and Klein expression for the singlet-triplet ground-state splitting |
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509 | (53) |
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Quantum Implementation of Symmetries |
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509 | (4) |
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510 | (2) |
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Behavior of the Ground State |
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512 | (1) |
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Mass Spectrum, Multiplets, and Goldstone Bosons |
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513 | (13) |
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The Octet Model of Gell-Mann and Ne'eman |
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513 | (6) |
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Isospin and unitary symmetry |
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Representations and weight diagrams |
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The mass formula of Gell-Mann and Okubo |
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Spontaneous Symmetry Breaking |
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519 | (7) |
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Instabilities from quantum corrections |
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526 | (14) |
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526 | (8) |
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Algebra of charges and currents |
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The sum rules of Cabibbo and Radicati, of Adler, and of Bjorken |
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Approximate Conservation of the Axial Current and Chiral Symmetry |
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534 | (2) |
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The pion as a Goldstone particle |
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Goldberger-Treiman relation and pion pole dominance |
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Low-Energy Theorems and Sum Rules |
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536 | (4) |
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Low-energy theorem for Compton scattering |
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Pion-nucleon scattering lengths and the Adler-Weisberger relation |
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540 | (9) |
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541 | (2) |
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The lagrangian of Gell-Mann and Levy |
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Explicit and spontaneous symmetry breaking |
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543 | (6) |
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549 | (13) |
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The π0 → 2γ Decay and Current Algebra |
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550 | (1) |
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The Veltman-Sutherland paradox |
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Axial Anomaly in the σ Model |
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551 | (5) |
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Explicit calculation of the Adler-Bell-Jackiw anomaly in a model |
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556 | (6) |
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562 | (70) |
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562 | (12) |
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The Gauge Field Aμ and the Tensor Fμν |
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563 | (4) |
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Geometrical interpretation |
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567 | (2) |
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Equations of motion and energy momentum tensor |
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Euclidean Solutions to the Classical Equations of Motion |
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569 | (4) |
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Degeneracy of the ground state and instantons |
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Gauge Invariance and Constraints |
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573 | (1) |
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Quantization of Gauge Fields |
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574 | (11) |
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574 | (3) |
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Integration over the Gauge Group |
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577 | (5) |
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The Faddeev-Popov determinant and ghosts |
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582 | (3) |
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Covariant and axial gauges |
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The Effective Action at the One-Loop Order |
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585 | (9) |
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585 | (3) |
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588 | (2) |
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590 | (3) |
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593 | (1) |
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Universality of coupling constant renormalization |
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594 | (12) |
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Slavnov-Taylor Identities |
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594 | (3) |
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Becchi-Rouet-Stora transformation |
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Identities for Proper Functions |
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597 | (2) |
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Recursive Construction of the Counterterms |
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599 | (5) |
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Gauge Dependence of Green Functions |
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604 | (1) |
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605 | (1) |
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606 | (14) |
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606 | (4) |
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Massive vector fields as intermediate bosons of weak or strong interactions |
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610 | (2) |
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Nonrenormalizability of massive vector theories |
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Spontaneous Symmetry Breaking |
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612 | (5) |
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Group theory of the Higgs phenomenon |
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The't Hooft-Polyakov monopole solutions |
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Renormalization of Spontaneously Broken Gauge Theories |
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617 | (2) |
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Gauge Independence and Unitarity of the S Matrix |
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619 | (1) |
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620 | (12) |
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620 | (4) |
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Electron-Neutrino Cross Sections |
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624 | (1) |
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625 | (2) |
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627 | (5) |
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632 | (59) |
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Effective Charge in Electrodynamics |
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633 | (8) |
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The Gell-Mann and Low Function |
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633 | (4) |
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The function ψ to lowest orders |
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The Callan-Symanzik Equation |
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637 | (4) |
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The β function in electrodynamics |
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641 | (13) |
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Scale and Conformal Invariance |
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642 | (3) |
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Classical scale invariance implies invariance under the full conformal group |
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645 | (6) |
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Derivation of the Callan-Symanzik equation in the general case |
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Callan-Symanzik Coefficients to Lowest Order |
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651 | (3) |
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Computation in Φ4 theory and nonabelian gauge fields |
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Scale Invariance Recovered |
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654 | (7) |
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654 | (3) |
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Ultraviolet and infrared fixed points |
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657 | (2) |
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Necessity of nonabelian gauge fields for asymptotic freedom |
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Leading logarithmic corrections |
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659 | (2) |
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Deep Inelastic Lepton-Hadron Scattering and Electron-Positron Annihilation into Hadrons |
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661 | (10) |
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661 | (3) |
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Scaling behavior of the structure functions |
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664 | (4) |
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Electron-Positron Annihilation |
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668 | (3) |
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The ratio R = σ e+e- → hadrons/σ e+e- → μ+μ- |
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Operator Product Expansions |
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671 | (20) |
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672 | (6) |
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Zimmermann's derivation on an example |
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Dominant and Subdominant Operators, Operator Mixing, and Conservation Laws |
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678 | (3) |
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681 | (10) |
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Wilson's expansion and the moments of the structure functions |
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691 | (10) |
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691 | (1) |
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A-2 Dirac Matrices and Spinors |
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692 | (4) |
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A-3 Normalization of States, S Matrix, Unitarity, and Cross Sections |
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696 | (2) |
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|
698 | (3) |
| Index |
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701 | |
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