QED in the Exact Renormalization Group

TL;DR

This paper investigates the behavior of QED within the exact renormalization group framework, analyzing gauge symmetry, Ward identities, and four-fermi interactions through perturbative solutions of flow and master equations.

Contribution

It provides a perturbative analysis of QED with momentum cutoff, revealing gauge symmetry features, Ward identities, and effects of four-fermi interactions on renormalization.

Findings

One-loop results confirm Ward identity $Z_1=Z_2$ without four-fermi interactions.

Four-fermi couplings modify the beta function and Ward identity.

Presence of a photon mass term due to regularization effects.

Abstract

The functional flow equation and the Quantum Master equation are consistently solved in perturbation for the chiral symmetric QED with and without four-fermi interactions. Due to the presence of momentum cutoff, unconventional features related to gauge symmetry are observed even in our perturbative results. In the absence of the four-fermi couplings, one-loop calculation gives us the Ward identity, $Z_{1}=Z_{2}$, and the standard results of anomalous dimensions and the beta function for the gauge coupling. It is a consequence of regularization scheme independence in one-loop computation. We also find a photon mass term. When included, four-fermi couplings contribute to the beta function and the Ward identity is also modified, $Z_{1} \neq Z_{2}$, due to a term proportional to the photon mass multiplied by the four-fermi couplings.