Multiloop Calculations in the String-Inspired Formalism: The Single Spinor-Loop in QED

TL;DR

This paper introduces a novel algorithm based on the worldline path-integral approach and supersymmetry to efficiently compute one-spinor-loop diagrams in QED, demonstrated through the two-loop beta function calculation.

Contribution

It develops a new method utilizing worldline supersymmetry and generalized Green functions for calculating spinor loop diagrams in QED.

Findings

Successfully computes the two-loop QED beta function

Provides an efficient algorithm for spinor loop diagram summation

Enhances the computational framework for quantum electrodynamics

Abstract

We use the worldline path-integral approach to the Bern-Kosower formalism for developing a new algorithm for calculation of the sum of all diagrams with one spinor loop and fixed numbers of external and internal photons. The method is based on worldline supersymmetry, and on the construction of generalized worldline Green functions. The two-loop QED $\beta$ -- function is calculated as an example.