The Theory of Photons and Electrons

Since the discovery of the corpuscular nature of radiation by Planck more than fifty years ago the quantum theory of radiation has gone through many stages of development which seemed to alternate between spectacular success and hopeless frustration. The most recent phase started in 1947 with the discovery of the electromagnetic level shifts and the realization that the exist ing theory, when properly interpreted, was perfectly adequate to explain these effects to an apparently unlimited degree of accuracy. This phase has now reached a certain conclusion: for the first time in the checkered history of this field of research it has become possible to give a unified and consistent presen tation of radiation theory in full conformity with the principles of relativity and quantum mechanics. To this task the present book is devoted. The plan for a book of this type was conceived during the year 1951 while the first-named author (J. M. J. ) held a Fulbright research scholarship at Cambridge University. During this year of freedom from teaching and other duties he had the opportunity of conferring with physicists in many different countries on the recent developments in radiation theory. The comments seemed to be almost unanimous that a book on quantum electrodynamics at the present time would be of inestimable value to physicists in many parts of the world. However, it was not until the spring of 1952 that work on the book began in earnest.

Inhalt
1 General Principles.- 2 the Radiation Field.- 3 Relativistic Theory of Free Electrons.- 4 Interaction of Radiation with Electrons.- 5 Invariance Properties of the Coupled Fields.- 6 Subsidiary Condition and Longitudinal Field.- 7 the S-Matrix.- 8 Evaluation of the S-Matrix.- 9 the Divergences in the Iteration Solution.- 10 Renormalization.- 11 the Photon-Electron System.- 12 the Electron-Electron System.- 13 the Photon-Photon System.- 14 Theory of the External Field.- 15 External Field Problems.- 16 Special Problems.- Mathematical Appendix.- Appendix A1 the Invariant Functions.- A1-1 The homogeneous delta-functions.- A1-2 The inhomogeneous delta-functions.- A1-3 Relations between the ?-functions.- A1-4 Integral representations.- A1-5 Explicit expressions.- A1-6 The S-functions.- Appendix A2 the Gamma-Matrices.- A2-1 Various representations.- A2-3 The amplitudes of the plane wave solutions.- A2-5 Spin sums.- A2-6 Polarization sums.- Appendix A3 a Theorem on the Representation of the Extended.- Lorentz Group by Irreducible Tensors.- Appendix A4 the Ordering Theorem.- A4-1 The ordering theorem for commuting fields.- A4-2 The ordering theorem for anticommuting fields.- A4-3 A generalization of the ordering theorem.- A4-4 The ordering of chronological products.- Appendix A5 on the Evaluation of Certain Integrals.- A5-1 Convergent integrals.- A5-2 Divergent integrals.- A5-3 The integral for the photon self-energy part.- A5-4 The integral for the electron self-energy part.- Appendix A6 a Limiting Relation for the ?-function.- Appendix A7 the Method of Analytic Continuation.- A7-1 The Bohr-Peierls-Placzek relation.- A7-2 The principle of limiting distance.- A7-3 The fundamental theorem on analytic continuation.- A7-4 Applications.- Appendix A8 Notation.- Supplement for theSecond Edition.- Supplement S1 Formulations of Quantum Electrodynamics.- S1-1 Lagrangian QFT.- S1-2 Axiomatic QFT.- S1-3 Locality, covariance, and indefinite metric.- S1-4 Lehmann-Symanzik-Zimmermann and related formalisms.- S1-5 Null plane QED.- References.- Supplement S2 Renormalization.- S2-1 Dyson-Salam-Ward renormalization.- S2-2 Bogoüubov-Parasiuk-Hepp-Zimmermann renormalization.- S2-3 Analytic renormalization.- References.- Supplement S3 Coherent States.- S3-1 A finite number of degrees of freedom.- S3-2 Coherent states of the radiation field.- S3-3 Application to ordering theorems.- References.- Supplement S4 Infrared Divergences.- S4-1 Dollard's discovery.- S4-2 A new picture.- S4-3 The asymptotically modified fields.- References.- Supplement S5 Predictions and Precision Experiments.- S5-1 The anomalous magnetic moment.- S5-2 The hyperfine structure of the hydrogen ground state.- S5-3 The Lamb-Retherford shift in hydrogen.- S5-4 Energy levels in positronium.- S5-5 Muonium hyperfine structure.- References.- Author Index.