A new path-integral solution to the Schwinger model

Abstract

It has been shown by the authors (see ref. 1) that it is necessary to supplement the conventional action of the Dirac fermion field with a boundary term. In this paper the Schwinger model (i.e., quantum electrodynamics in two space-time dimensions with massless fermions) is solved through the path integral with the boundary term included in the action. This considerably complicates the evaluation of the path integral so that only partial integrations over the field variables are attempted here. In the case of the integration over the electromagnetic potential Au, A0 will be set to zero based on arguments from a formulation of generalized Hamiltonian mechanics by one of the authors (Ray Skinner).