Two-Loop Diagrams in Causal Perturbation Theory

TL;DR

This paper revisits the scalar two-loop master diagram in causal perturbation theory, expressing propagators as double integrals and highlighting the method's advantages over traditional Feynman integral calculations.

Contribution

It demonstrates how the causal method simplifies two-loop diagram calculations in QED and QCD, providing explicit integral representations and solutions.

Findings

Vacuum polarization integrals expressed with polylogarithms

Fermion propagator integral not reducible to known functions

Causal method offers a straightforward alternative to Feynman integrals

Abstract

The scalar two-loop master diagram is revisited in the massive cases needed for the computation of boson and fermion propagators in QED and QCD. By means of the causal method it is possible in a straightforward manner to express the propagators as double integrals. 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 advantage of the method in comparison with Feynman integral calculations is indicated.