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Stochastic regularization of fermions

Journal Article · · Phys. Rev. D; (United States)
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Stochastic quantization is applied to the U(1)-gauge theory including fermions (QED). The early formulation of stochastically quantized QED used non-gauge-invariant Langevin equations, whereas nowadays the explicitly gauge-invariant equations of Ishikawa are preferred. We will comment on the older representation, where gauge invariance can be violated by the regularization because gauge invariance is already broken by the Langevin equations from the beginning. This is explicitly demonstrated in a few examples, including anomalous Ward-Takahashi identities and the vacuum polarization tensor Pi/sub munu/. Deeper insight into the breakdown of gauge invariance is gained by the use of the Fokker-Planck equation and the construction of equilibrium probability distributions in the case of a classical electromagnetic background field. Our investigations result in the conclusion that only Ishikawa's explicitly gauge-invariant Langevin equations can be applied without contradictions.

Research Organization:
Ruhr-Universitaet Bochum, Institut fuer Theoretische Physik 11, 4630 Bochum 1, Federal Republic of Germany
OSTI ID:
5891147
Journal Information:
Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 33:8; ISSN PRVDA
Country of Publication:
United States
Language:
English

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Related Subjects

645201 -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CORRELATION FUNCTIONS
DIFFERENTIAL EQUATIONS
ELECTRODYNAMICS
ELECTROMAGNETIC FIELDS
EQUATIONS
FERMIONS
FIELD THEORIES
FOKKER-PLANCK EQUATION
FUNCTIONS
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LANGEVIN EQUATION
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILITY
QUANTIZATION
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
STOCHASTIC PROCESSES
VACUUM POLARIZATION
WARD IDENTITY