Anomalies of the Axial-Vector Current in Two Dimensions

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Abstract
In a world with one space and one time dimension, it is shown that the axial-vector current in a vectorgluon model exhibits anomalies in perturbation theory analogous to those found by Adler in fermion electrodynamics. The analysis is extended to include a four-fermion (Thirring) interaction; this model has been solved exactly by Sommerfield, permitting an explicit verification of the perturbation-theory calculations. In analogy to results in four dimensions, a model is presented in which the anomalous properties of the axial-vector current, both in its divergence and in its commutation relations, follow immediately from the canonical structure of the theory.