Higher-Order Covariant Feynman Diagrams

Abstract

In this final chapter we investigate the consequences of higher-order loop diagrams, first justifying their necessity and describing a pragmatic “regularization” procedure for circumventing unphysical infinities inherent in many loop integrals. Next we work out in detail the finite second-order anomalous-magnetic-moment radiative corrections for the electron and point out where other finite triangle-type loop diagrams lead to interesting results. Then we compute all of the second-order QED self-energy and vertex-modification loop integrals, showing how the resulting infinities cancel in the final form for the O(e²) dressed-electron form factors and applying the latter to calculate the Lamb shift in atomic hydrogen. To give the reader a feeling for the rigor required to handle properly loop infinities, we briefly survey the renormalization program in field theory and also develop an alternate dispersion-theoretic interpretation of Feynman diagrams in general and QED loop graphs in particular. Finally we use dispersion theory to investigate the strong-interaction S-matrix, presumably corresponding to summing over large classes of Feynman diagrams. Dispersion relations for proton Compton and pion—nucleon scattering reveal the method, with the additional formalisms of current algebra and Regge poles describing the low- and high-energy behavior of dispersion integrals.