Anomalies from stochastic quantization and their path-integral interpretation

Journal Article · Mon Jan 15 04:00:00 EST 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.41.553· OSTI ID:6915937

Morita, K ^[1]; Kase, H ^[2]

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1. Department of Physics, Nagoya University, Nagoya 464-01, Japan (JP)
2. Department of Physics, Daido Institute of Technology, Nagoya 457, (Japan)

The regularized generating functional in Euclidean stochastic quantization of Dirac theory in a background field is derived in both Markovian and non-Markovian stochastic regularization schemes to show the existence of the equilibrium limit under the same condition as in the unregularized theory. Contrary to the latter case, however, the equilibrium limit depends on an arbitrary kernel in the fermion Langevin equation, which confirms our previous result on the kernel dependence of anomalies in an external gauge field. In addition to the known kernels yielding the consistent and covariant anomalies, a new kernel is proposed, which leads to a consistent form in {ital D}=2 dimensions and a new form in {ital D}=4. The relation to Fujikawa's path-integral method is also discussed, where the kernel introduces, in general, non-Hermitian operators which are treated by the plane-wave fermion measure and the regularized transformations of Bern {ital et} {ital al}., now depending on the kernel.

• OSTI ID: 6915937
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 41:2; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
EUCLIDEAN SPACE
FERMIONS
LANGEVIN EQUATION
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
QUANTIZATION
RIEMANN SPACE
SPACE
STOCHASTIC PROCESSES
WAVE EQUATIONS