Dynamical Fermion Masses and Constraints of Gauge Invariance in Quenched QED3

Abstract

Numerical study of the Schwinger-Dyson equation (SDE) for the fermion propagator (FP) to obtain dynamically generated chirally asymmetric solution in an arbitrary covariant gauge $ξ$ is a complicated exercise specially if one employs a sophisticated form of the fermion-boson interaction complying with the key features of a gauge field theory. However, constraints of gauge invariance can help construct such a solution without having the need to solve the Schwinger-Dyson equation for every value of $ξ$. In this article, we propose and implement a method to carry out this task in quenched quantum electrodynamics in a plane (QED3). We start from an approximate analytical form of the solution of the SDE for the FP in the Landau gauge. We consider the cases in which the interaction vertex (i) is bare and (ii) is full. We then apply the Landau-Khalatnikov-Fradkin transformations (LKFT) on the dynamically generated solution and find analytical results for arbitrary value of $ξ$. We also compare our results with exact numerical solutions available for a small number of values of $ξ$ obtained through a direct analysis of the corresponding SDE.