Anomalies in spaces of even and odd dimensions in the scheme of stochastic quantization

Abstract

Axial anomalies in spaces of even and odd dimensions are studied by the method of stochastic quantization with a generalized scheme of stochastic regularization. Although the stochastic regularization formally preserves the axial and gauge symmetries, the standard even-dimensional axial anomalies of Dirac fermions are correctly reproduced in the limit in which the regularization is lifted, while the anomalies of the chiral fermions are reproduced in covariant form. An analysis is also made of the general conditions for the existence and canceling of anomalies of massless fermions that violate parity in odd-dimensional spaces. The stochastic scheme works in odd-dimensional spaces when the parity-violating anomalies are absent. The P-anomalous part of the effect action of infinitely heavy fermions in odd-dimensional spaces is calculated explicitly.