Abstract
The commutativity of the limits of the fermion mass going to zero and the stochastic time going to infinity in the derivation of local and global anomalies by the stochastic quantization method is analyzed. For the case of chiral anomalies the limits are shown to commute, contrary to the parity anomaly case where the limits do not commute and no anomaly is apparent when the massless limit is taken first. This does not mean, however, that stochastic quantization cannot reproduce parity anomalies, or that parity can be preserved in such theories. The physical interpretation of this result is shown to be the fact that a statistical mixture of two theories is obtained in this limit as opposed to a pure theory.
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