Implicit regularization beyond one loop order: gauge field theories

TL;DR

This paper extends a regularization method for gauge theories beyond one loop, demonstrating its effectiveness through calculations in QED and deriving the two-loop beta-function.

Contribution

It introduces a constrained version of Implicit Regularization applicable beyond one loop in gauge theories, maintaining gauge invariance via finite surface terms.

Findings

Successfully applied CIR to two-loop calculations in QED

Derived the two-loop beta-function for spinorial QED

Maintained Ward identities through finite surface terms

Abstract

We extend a constrained version of Implicit Regularization (CIR) beyond one loop order for gauge field theories. In this framework, the ultraviolet content of the model is displayed in terms of momentum loop integrals order by order in perturbation theory for any Feynman diagram, while the Ward-Slavnov-Taylor identities are controlled by finite surface terms. To illustrate, we apply CIR to massless abelian Gauge Field Theories (scalar and spinorial QED) to two loop order and calculate the two-loop beta-function of the spinorial QED.