BRST Current Algebra Derivation of the Higher Cocycles

Abstract

Two topics of much current research in mathematical physics are the BRST quantization of gauge theories and the understanding of anomalies in gauge theories. While a large part of the stimulus for this research is the revival of interest in string theory, much remains to be learned about gauge theories. Here, we shall present a new extension of BRST symmetry in the form of a local symmetry and demonstrate that this leads to an understanding, in the context of a field theory, of the higher cocycles that have been mathematically associated with chiral anomalies.¹ We obtain, furthermore, a unification of many approaches to the chiral anomaly. Namely, once the BRST symmetry is gauged, we can examine BRST current algebra. Anomalies and the cocyles associated with them are consequences of this current algebra. Moreover, the BRST charge derived from the BRST current is not nilpotent.