Functional flows in QED and the modified Ward-Takahashi identity

TL;DR

This paper investigates the modified Ward-Takahashi identity within the functional renormalisation group framework for QED, deriving explicit form factors for the Wilsonian effective action and connecting them to the 1PI effective action.

Contribution

It provides a partial solution to the modified Ward-Takahashi identity for the Wilsonian effective action in QED, including explicit calculations of the photon two-point function.

Findings

Computed the longitudinal photon two-point vertex function with cutoff dependence.

Derived form factors from the modified Ward-Takahashi identity.

Connected Wilsonian effective action results to the 1PI effective action.

Abstract

In the functional renormalisation group approach to gauge theory, the Ward-Takahashi identity is modified due to the presence of an infrared cutoff term. It take the most accessible form for the Wilsonian effective action. In the present work we solve these identities, partially, for the Wilson effective action of QED. In particular, we compute the longitudinal part of the photon two point vertex function as a momentum- dependent function in the presence of the cutoff k. The resultant Wilsonian effective action carries form factors that originate from the modified Ward-Takahashi identity. We show how this result carries over to the one-particle-irreducible effective action.