Effective Action for QED with Fermion Self-Interaction in D=2 and D=3 Dimensions

TL;DR

This paper investigates how quartic fermion self-interactions affect the effective action and photon propagators in QED in two and three dimensions, revealing the emergence of massive poles and screening effects in the static potential.

Contribution

It provides a nonperturbative analysis of the effective action in QED with Thirring-type interactions, including numerical determination of photon propagator poles and static potential behavior.

Findings

In D=2, a massive pole can appear for strong Thirring coupling.

In D=3, multiple pole configurations are possible, including no poles.

The Thirring interaction introduces a screening term in the static potential.

Abstract

In this work we discuss the effect of the quartic fermion self-interaction of Thirring type in QED in D=2 and D=3 dimensions. This is done through the computation of the effective action up to quadratic terms in the photon field. We analyze the corresponding nonlocal photon propagators nonperturbatively in % \frac{k}{m}, where k is the photon momentum and m the fermion mass. The poles of the propagators were determined numerically by using the Mathematica software. In D=2 there is always a massless pole whereas for strong enough Thirring coupling a massive pole may appear . For D=3 there are three regions in parameters space. We may have one or two massive poles or even no pole at all. The inter-quark static potential is computed analytically in D=2. We notice that the Thirring interaction contributes with a screening term to the confining linear potential of massive QED_{2}. In D=3 the static potential must be calculated numerically. The screening nature of the massive QED$_{3}$ prevails at any distance, indicating that this is a universal feature of % D=3 electromagnetic interaction. Our results become exact for an infinite number of fermion flavors.