Effective action for QED with fermion self-interaction in D = 2 and D = 3 dimensions

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 k/m, where k is the photon momentum and in 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 parameter space. We may have one or two massive poles or even no pole at all. The interquark 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 two-dimensional QED (QED2). 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. © 2002 The American Physical Society.