Abstract
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 inconsistently quantized in the stochastic scheme unless the parity-violating anomales cancel.
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Nissimov, E.R., Pacheva, S.J. Nonperturbative inconsistency of stochastic quantization in odd dimensions. Lett Math Phys 13, 219–227 (1987). https://doi.org/10.1007/BF00423449
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DOI: https://doi.org/10.1007/BF00423449