Two-Loop Diagrams in Causal Perturbation Theory

✍ Scribed by Andreas Aste

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 521 KB
• Volume: 257
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1997.5686

✦ Synopsis

Scalar two-loop diagrams are calculated analytically in massive cases needed for the computation of boson and fermion propagators in QED and QCD by the causal method of Epstein and Glaser. It is demonstrated that this method, which is the basis for the so-called dispersive methods, provides many advantages for higher loop calculations in comparison to the usual Feynman integrals. It is possible to express the propagators as double integrals in a straightforward manner. In the case of vacuum polarization both integrations can be carried out in terms of polylogarithms, whereas the last integral in the fermion propagator cannot be expressed by known special functions. The infrared problems in connection with the adiabatic limit are carefully discussed. 1997 Academic Press Contents 1. The causal approach to quantum field theory. 1.1. Introduction. 2. The causal construction of perturbative quantum field theory. 2.1. General properties of the causal method. 2.2. The theory of distribution splitting. 3. The calculation of two-loop diagrams in causal perturbation theory. 3.1. Introduction. 3.2. Vacuum polarization in fourth order. 3.3. The electron propagator in fourth order. 4. The remaining two-loop diagrams. 4.1. Vacuum polarization. 4.2. The electron propagator. Appendix A: Free fields, commutation relations, and propagators. Appendix B: Useful relations for the calculation of 2-loop diagrams.