Ward-Takahashi Identity in Denominator Regularization at One Loop

TL;DR

This paper derives explicit one-loop electron self-energy and vertex correction expressions in QED using denominator regularization, demonstrating that gauge symmetry via Ward-Takahashi identity is preserved in this scheme.

Contribution

It introduces and applies denominator regularization to QED one-loop calculations, showing gauge invariance is maintained, which is a novel aspect of this regularization method.

Findings

Explicit analytic expressions for self-energy and vertex correction.

Demonstration that Ward-Takahashi identity holds in denominator regularization.

Regularization scheme preserves gauge symmetry.

Abstract

Explicit analytic expressions for the electron self-energy and the vertex correction in quantum electrodynamics are derived at one loop using the recently proposed regularization scheme known as denominator regularization, assisted by its correspondence with dimensional regularization to determine the coefficient functions, which are a specific ingredient of this approach. We then show that the regularized amplitudes satisfy the Ward-Takahashi identity, thereby ensuring that gauge symmetry is preserved after regularization.