The arbitrariness induced by the regularization of the fermion functional in two-dimensional U(1) gauge theories with a massless fermion is discussed in detail. It is shown that under very general assumptions the only consistent model with a gauge-invariant action is the gauge-invariant Schwinger model. An action with a mass term for the gauge field is needed in order to reproduce the consistent chiral Schwinger model.

• Received 26 June 1989

DOI:https://doi.org/10.1103/PhysRevD.41.2568