The Theory of Photons and Electrons - The Relativistic Quantum Field Theory of Charged Particles with Spin One-half

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PREFACE TO THE FIRST EDITION......Page 4 PREFACE TO THE SECOND EDITION......Page 9 Contents......Page 12 1-1 The natural unit system......Page 17 1-2 Some fundamental notions of the special theory of relativity......Page 18 1-3 Some basic notions of quantum mechanics......Page 21 1-4 Localizability......Page 23 1-5 Observables of a field......Page 24 1-6 Canonical transformations......Page 26 1-7 Lorentz transformations as canonical transformations......Page 27 1-8 The action principle......Page 30 1-9 The equation of motion......Page 34 1-10 Momentum operators......Page 35 1-11 Conservation laws......Page 36 1-12 Commutation rules......Page 38 2-1 The classical field equations......Page 41 2-2 The associated boundary value problem......Page 43 2-4 Quantization of the radiation field......Page 44 2-5 Momentum operators for the radiation field......Page 47 2-6 Plane wave decomposition of the radiation field......Page 51 2-7 Explicit representations of the field operators......Page 53 2-8 The spin of the photon......Page 56 2-9 Definition of the vacuum......Page 63 3-1 The field equations for the one-particle problem......Page 66 3-2 The associated boundary value problem......Page 67 3-3 Relativistic invariance of the field equations......Page 68 3-4 The bilinear covariants......Page 69 3-6 Quantization......Page 72 3-7 Momentum operators......Page 75 3-8 Plane wave decomposition......Page 76 3-9 Explicit representation of the field operators......Page 81 3-10 The definition of the vacuum......Page 83 4-1 The field equations......Page 85 4-2 Commutation rules for the interacting fields......Page 89 4-3 The interaction picture......Page 92 4-4 Measurability of the fields......Page 94 5-1 Proper Lorentz transformations......Page 98 5-2 Gauge transformations......Page 99 5-3 Space inversion......Page 102 5-4 Time inversion......Page 104 5-5 Charge conjugation......Page 110 5-6 Scale transformations......Page 112 6-1 The covariant Coulomb interaction......Page 113 6-2 The subsidiary condition and the construction of the state vector......Page 116 6-3 The Gupta method......Page 119 6-4 Gauge-independent interaction......Page 126 6-5 Radiation fields with finite mass......Page 129 7-1 Preliminary definition of the S-matrix......Page 133 7-2 The wave matrix......Page 136 7-3 The wave operator......Page 142 7-4 Integral representation of the wave operator......Page 145 7-5 Definition of the S-matrix......Page 147 7-6 Invariance properties of the S-matrix......Page 152 8-1 The iteration solution......Page 160 8-2 The Feynman-Dyson diagrams......Page 162 8-3 Diagrams in momentum space......Page 167 8-4 Closed loops......Page 175 8-5 The substitution law......Page 177 8-6 Lifetimes and cross sections......Page 179 8-7 Evaluation of the S-matrix in the Heisenberg picture......Page 183 Chapter 9 The Divergences in the Iteration Solution......Page 186 9-1 Historical background......Page 187 9-2 Classification of divergences......Page 189 9-3 The vacuum fluctuations......Page 192 9-4 The self-energy of the electron......Page 194 9-5 The self-energy of the photon......Page 204 9-6 The vertex part......Page 213 10-1 The primitive divergences......Page 219 10-2 Irreducible and proper diagrams......Page 222 10-3 Separation of divergences in irreducible parts......Page 226 10-4 Separation of divergences in reducible parts......Page 227 10-6 Charge renormalization......Page 235 10-7 Wave function renormalization......Page 237 10-8 Sufficiency proof......Page 238 10-9 Regulators......Page 239 Chapter 11 The Photon-Electron System......Page 244 11-1 Compton scattering......Page 245 11-2 Double Compton scattering......Page 251 11-3 Radiative corrections to Compton scattering......Page 257 11-4 Pair production in photon-electron collisions......Page 263 12-1 Mpller scattering......Page 268 12-2 Bhabha scattering......Page 273 12-3 Bremsstrahlung in electron-electron collisions......Page 277 12-4 Annihilation of free negaton-positon paIrS......Page 279 12-5 Positronium; selection rules......Page 290 12-6 Positronium annihilation......Page 298 13-1 Photon-photon scattering as part of a diagram......Page 303 13-2 Photon-photon scattering cross sections......Page 308 13-3 Pair production in photon-photon collision......Page 315 Chapter 14 Theory of the External Field......Page 318 14-1 The external field approximation......Page 319 14-2 The bound interaction picture......Page 322 14-3 Commutation rules......Page 324 14-4 The electron propagation function......Page 328 14-5 The S-matrix in the external field approximation......Page 334 14-6 Renormalization......Page 337 14-7 Cross sections and energy levels......Page 338 15-1 Coulomb scattering......Page 343 15-2 Radiative corrections to Coulomb scattering......Page 348 15-3 The magnetic moment of the election......Page 358 15-4 Energy levels in hydrogen-like atoms......Page 361 15-5 Radiative transitions between bound states......Page 377 15-6 Bremsstrahlung......Page 380 15-7 Pair production and annihilation......Page 389 15-8 Delbruck and Rayleigh scattering......Page 395 16-1 The infrared divergences......Page 406 16-2 Radiation damping in collision processes......Page 421 16-3 The natural line width of stationary states......Page 424 16-4 The self-stress of the electron......Page 426 16-5 Outlook......Page 431 Appendix A1 THE INVARIANT FUNCTIONS......Page 434 A1-2 The inhomogeneous delta-functions......Page 435 A1-3 Relations between the Δ-functions......Page 436 A1-4 Integral representations......Page 438 A1-6 The S-functions......Page 439 A2-1 Various representations......Page 440 A2-2 The matrices A, B, and C......Page 444 A2-3 The amplitudes of the plane wave solutions......Page 446 A2-4 A theorem on the traces of γ-matrices......Page 451 A2-5 Spin sums......Page 453 A2-6 Polarization sums......Page 454 Appendix A3 A THEOREM ON THE REPRESENTATION OF THE EXTENDED LORENTZ GROUP BY IRREDUCIBLE TENSORS......Page 456 A4-1 The ordering theorem for commuting fields......Page 460 A4-2 The ordering theorem for anticommuting fields......Page 464 A4-4 The ordering of chronological products......Page 466 Appendix A5 ON THE EVALUATION OF CERTAIN INTEGRALS......Page 469 A5-1 Convergent integrals......Page 470 A5-2 Divergent integrals......Page 472 A5-3 The integral for the photon self-energy part......Page 475 A5-4 The integral for the electron self-energy part......Page 478 Appendix A6 A LIMITING RELATION FOR THE δ-FUNCTION......Page 479 A7-1 The Bohr-Peierls-Placzek relation......Page 480 A7-2 The principle of limiting distance......Page 483 A7-3 The fundamental theorem on analytic continuation......Page 484 A7-4 Applications......Page 488 Appendix A8 NOTATION......Page 491 Supplement S1 FORMULATIONS OF QUANTUM ELECTRODYNAMICS......Page 493 S1-1 Lagrangian QFT......Page 494 S1-2 Axiomatic QFT......Page 495 S1-3 Locality, covariance, and indefinite metric......Page 497 S1-4 Lehmann-Symanzik-Zimmermann and related formalisms......Page 500 S1-5 Null plane QED......Page 504 References......Page 506 S2-1 Dyson-Salam-Ward renormalization......Page 510 S2-2 Bogoliubov-Parasiuk-Hepp-Zimmermann renormalization......Page 513 S2-3 Analytic renormalization......Page 515 References......Page 516 S3-1 A finite number of degrees of freedom......Page 517 S3-2 Coherent states of the radiation field......Page 520 S3-3 Application to ordering theorems......Page 523 References......Page 525 S4-1 Dollard's discovery......Page 527 S4-2 A new picture......Page 528 S4-3 The asymptotically modified fields......Page 533 S4-4 The new S-matrix......Page 539 References......Page 543 S5-1 The anomalous magnetic moment......Page 544 S5-2 The hyperfine structure of the hydrogen ground state......Page 545 S5-3 The Lamb-Retherford shift in hydrogen......Page 547 S5-4 Energy levels in positronium......Page 549 S5-5 Muonium hyperfine structure......Page 550 References......Page 551 Author Index......Page 554 Subject Index......Page 560