Nonperturbative inconsistency of stochastic quantization in odd dimensions (Q580801)

It is shown that a stochastically quantized theory of interacting fermion and gauge fields in odd spacetime dimensions can be renormalized, preserving both gauge- and parity-invariance. Thus, the pertinent parity- violating anomalies are not reproduced by the stochastic quantization. Moreover, this theory does not possess a nonperturbative equilibrium limit unless one introduces an appropriate parity-violating counterterm. We conclude that an odd-dimensional gauge theory with fermions cannot be consistently quantized in the stochastic scheme unless the parity- violating anomalies cancel.