Worldline Green Functions for Multiloop Diagrams

TL;DR

This paper extends the Bern-Kosower formalism to multiloop diagrams using worldline Green functions, enabling more compact representations of Feynman diagrams in scalar and abelian gauge theories.

Contribution

It introduces a multiloop generalization of the Bern-Kosower formalism with explicit Green functions for complex diagrams, enhancing computational efficiency.

Findings

Explicit Green functions constructed for two-loop graphs.

Integral representations unify classes of Feynman diagrams.

Facilitates compact expressions in scalar and abelian gauge theories.

Abstract

We propose a multiloop generalization of the Bern-Kosower formalism, based on Strassler's approach of evaluating worldline path integrals by worldline Green functions. Those Green functions are explicitly constructed for the basic two-loop graph, and for a loop with an arbitrary number of propagator insertions. For scalar and abelian gauge theories, the resulting integral representations allow to combine whole classes of Feynman diagrams into compact expressions.