Lattice fermions in the Schwinger model

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Abstract
We obtain exact solutions for the continuum limit of the lattice Schwinger model, using the Lagrangian formulations of the Wilson, ‘‘naive,’’ Kogut-Susskind, and Drell-Weinstein-Yankielowicz (DWY) lattice fermion derivatives. We examine the mass gap, the anomaly, and the chiral order parameter 〈ψ¯ψ〉. As expected, our results for the Wilson formulation are consistent with those of the continuum theory and our results for the ‘‘naive’’ formulation exhibit spectrum doubling. In the Kogut-Susskind case, the U(1) anomaly is doubled, but 〈ψ¯ψ〉 vanishes. In solving the DWY version of the model, we make use of a proposal for resumming perturbation theory due to Rabin. The Lagrangian formulation of the DWY Schwinger model displays spectrum doubling and a mass gap that is √2 times the continuum one. The U(1) anomaly graph is nonvanishing and noncovariant in the continuum limit, but has a vanishing divergence. The chiral order parameter 〈ψ¯ψ〉 also vanishes.