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

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