XVI Table of Contents 14.5 Calculation of the Photon Propagator.....................316 Problems..................................................320 15.Interacting Fields,Quantum Electrodynamics ............321 15.1 Lagrangians,Interacting Fields..... 321 15.1.1 Nonlinear Lagrangians 321 15.1.2 Fermions in an External Field. 322 15.1.3 Interaction of Electrons with the Radiation Field: 322 15.2 The Int Quantu on Rer Pertu bation 292 01 The Int eracti 15.2.2 Perturbation Theory.......... 32 15.3 The S Matrix. 328 15.3.1 General Formulation............................. 328 15.3.2 Simple Transitions. 332 *15.4 Wick's Theorem 335 15.5 Simple Scattering Processes,Feynman Diagrams 220 15.5.1 The First-Order Term .220 341 15.5.3 Second-Order 346 15.5.4 Feynman Rules of Quantum Electrodynamics........356 15.6 Radiative Corrections... 。。。。。。。。。。。。。。。。。。。。。350 15.6.1 The Self-Energy of the Electron....................359 15.6.2 Self-Energy of the Photon,Vacuum Polarization.... 365 15.6.3 Vertex Corrections .... 366 15.6.4 The Ward Identity and Charge renormalization 36R 15.6.5 Anomalous Magnetic Moment of the Electron....... 271 Problem 373 Bibliography for Part III. 375 Appendix. 377 Alternative Derivation of the Dirac Equation. .377 B Dirac Matrice 370 ard Represe ntation 379 Chiral Representation 37 B.3 Majorana Representations ....................... Projection Operators for the Spin.................... Definition.. 380 0.2 Rest frame. 380 03 General Significance of the Projection Operator P(n).381 D The Path-Integral Representation of Quantum Mechanics. .385 of the Electromagnetic Field, -Bleuler Method 3R7 E.1 Quantization and the Feynman Propagator.. 8>XVI Table of Contents 14.5 Calculation of the Photon Propagator . . . . . . . . . . . . . . . . . . . . . 316 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 15. Interacting Fields, Quantum Electrodynamics ............ 321 15.1 Lagrangians, Interacting Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 15.1.1 Nonlinear Lagrangians . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 15.1.2 Fermions in an External Field . . . . . . . . . . . . . . . . . . . . . . 322 15.1.3 Interaction of Electrons with the Radiation Field: Quantum Electrodynamics (QED) . . . . . . . . . . . . . . . . . . 322 15.2 The Interaction Representation, Perturbation Theory . . . . . . . 323 15.2.1 The Interaction Representation (Dirac Representation) 324 15.2.2 Perturbation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327 15.3 The S Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 15.3.1 General Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 15.3.2 Simple Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 ∗15.4 Wick’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335 15.5 Simple Scattering Processes, Feynman Diagrams . . . . . . . . . . . 339 15.5.1 The First-Order Term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 15.5.2 Mott Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 15.5.3 Second-Order Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 15.5.4 Feynman Rules of Quantum Electrodynamics . . . . . . . . 356 ∗15.6 Radiative Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358 15.6.1 The Self-Energy of the Electron . . . . . . . . . . . . . . . . . . . . 359 15.6.2 Self-Energy of the Photon, Vacuum Polarization . . . . . . 365 15.6.3 Vertex Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366 15.6.4 The Ward Identity and Charge Renormalization . . . . . . 368 15.6.5 Anomalous Magnetic Moment of the Electron . . . . . . . . 371 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 Bibliography for Part III ..................................... 375 Appendix ..................................................... 377 A Alternative Derivation of the Dirac Equation . . . . . . . . . . . . . . . 377 B Dirac Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 B.1 Standard Representation . . . . . . . . . . . . . . . . . . . . . . . . . . 379 B.2 Chiral Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379 B.3 Majorana Representations . . . . . . . . . . . . . . . . . . . . . . . . . 380 C Projection Operators for the Spin . . . . . . . . . . . . . . . . . . . . . . . . 380 C.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 C.2 Rest Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 C.3 General Significance of the Projection Operator P(n) . 381 D The Path-Integral Representation of Quantum Mechanics . . . . 385 E Covariant Quantization of the Electromagnetic Field, the Gupta–Bleuler Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387 E.1 Quantization and the Feynman Propagator . . . . . . . . . . 387