Stochastic regularization of fermions
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), Vol. 33:8
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
FERMIONS
QUANTIZATION
QUANTUM ELECTRODYNAMICS
GAUGE INVARIANCE
CORRELATION FUNCTIONS
ELECTROMAGNETIC FIELDS
FOKKER-PLANCK EQUATION
LANGEVIN EQUATION
PROBABILITY
STOCHASTIC PROCESSES
VACUUM POLARIZATION
WARD IDENTITY
DIFFERENTIAL EQUATIONS
ELECTRODYNAMICS
EQUATIONS
FIELD THEORIES
FUNCTIONS
INVARIANCE PRINCIPLES
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
645400* - High Energy Physics- Field Theory
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