Relation between Worldline Green Functions for Scalar Two-Loop Diagrams

TL;DR

This paper explores the relationship between two different parametrizations of two-loop bosonic worldline Green functions, revealing transformation rules based on reparametrizations of proper time and modular parameters.

Contribution

It establishes a connection between two forms of two-loop Green functions through transformation rules, enhancing understanding of their equivalence under reparametrizations.

Findings

Green functions are related by specific transformation rules

Reparametrizations connect different Green function parametrizations

Enhances understanding of two-loop worldline Green functions

Abstract

We discuss a relation between two-loop bosonic worldline Green functions which are obtained by Schmidt and Schubert in two different parametrizations of a two-loop worldline. These Green functions are transformed into each other by some transformation rules based on reparametrizations of the proper time and worldline modular parameters.