δ expansion for local gauge theories. II. Nonperturbative calculation of the anomaly in the Schwinger model

This is the second paper in a series in which we show how to use the principles of the δ expansion to obtain nonperturbative solutions to gauge theories. The approach consists of replacing the usual minimal-coupling term bar ψ(i∂-eA)ψ by bar ψ(i∂-eA)δψ and then expanding the new theory in powers of δ. For all values of δ the theory is locally gauge invariant. Thus, local gauge invariance holds order by order in powers of δ. In this paper we show how to calculate the photon propagator and thus the anomaly in the Schwinger model (two-dimensional massless quantum electrodynamics) to first order in δ. At δ=1 the exact value for the anomaly, e2/π, is obtained