Quantum dynamics of chiral fermions in a model with anomalous breaking of gauge invariance

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Abstract
We study the quantum dynamics of chiral fermion fields minimally coupled to a gauge field. The model, originally proposed by Jackiw and Rajaraman, is known to exhibit the anomalous breaking of gauge invariance, which leads to the appearance of an arbitrary parameter a. Both functional and operator techniques are used to obtain the two-point fermion Green’s functions for a>1 and a=1. In both cases clustering holds, and the theory contains asymptotically free fermions. The quantum equation of motion for the field tensor resembles formally that of the Proca theory, but with a dynamically generated mass and a nonconserved source. It is found that for a=1 the generating functional cannot be written in terms of a manifestly Lorentz-invariant Lagrangian.