Continuum regularization of quantum field theory
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); California Univ., Berkeley (USA). Dept. of Physics
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 7104107
- Report Number(s):
- LBL-22303; ON: DE87002549
- Resource Relation:
- Other Information: Thesis. Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
Similar Records
Continuum regularized Yang-Mills theory
Evaluation of the chiral anomaly by the stochastic quantization method
Related Subjects
QUANTUM FIELD THEORY
GAUGE INVARIANCE
LANGEVIN EQUATION
LORENTZ INVARIANCE
ACTION INTEGRAL
ELECTRODYNAMICS
GLUONS
QUANTIZATION
REST MASS
STOCHASTIC PROCESSES
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORIES
INTEGRALS
INVARIANCE PRINCIPLES
MASS
POSTULATED PARTICLES
645400* - High Energy Physics- Field Theory