QED in the worldline representation

TL;DR

This paper reviews recent developments in the worldline representation of quantum electrodynamics (QED), highlighting three computational techniques: string-inspired formalism, worldline Monte Carlo, and worldline instantons.

Contribution

It provides a concise overview of three innovative methods for evaluating worldline path integrals in QED, enhancing computational approaches in the field.

Findings

String-inspired formalism using worldline Green functions

Worldline Monte Carlo for numerical evaluations

Semiclassical worldline instanton approach

Abstract

Simultaneously with inventing the modern relativistic formalism of quantum electrodynamics, Feynman presented also a first-quantized representation of QED in terms of worldline path integrals. Although this alternative formulation has been studied over the years by many authors, only during the last fifteen years it has acquired some popularity as a computational tool. I will shortly review here three very different techniques which have been developed during the last few years for the evaluation of worldline path integrals, namely (i) the ``string-inspired formalism'', based on the use of worldline Green functions, (ii) the numerical ``worldline Monte Carlo formalism'', and (iii) the semiclassical ``worldline instanton'' approach.