World-line Green functions with momentum and source conservations

TL;DR

This paper introduces a new constraint on the source function in the world-line formalism, ensuring unique Green functions by mimicking momentum conservation, and discusses reparametrizations of world-line diagrams.

Contribution

It proposes a novel constraint on the source function that enforces momentum conservation-like conditions, leading to uniquely defined Green functions in the world-line approach.

Findings

The constraint effectively removes ambiguities in Green functions.

Reparametrization invariance of world-line diagrams is analyzed.

The method simplifies calculations of loop Green functions.

Abstract

Based on the generating functional method with an external source function, a useful constraint on the source function is proposed for analyzing the one- and two-loop world-line Green functions. The constraint plays the same role as the momentum conservation law of a certain nontrivial form, and transforms ambiguous Green functions into the uniquely defined Green functions. We also argue reparametrizations of the Green functions defined on differently parameterized world-line diagrams.