 
Summary: annals of physics 257, 158 204 (1997)
TwoLoop Diagrams in Causal Perturbation Theory
Andreas Aste*
Institut fur Theoretische Physik, Universitat Zurich, Winterthurerstrasse 190,
CH8057 Zurich, Switzerland
Received December 27, 1996
Scalar twoloop diagrams are calculated analytically in massive cases needed for the com
putation 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 socalled
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 twoloop diagrams in causal perturbation theory. 3.1. Introduction.
