Continuum regularization of quantum field theory

Technical Report · Tue Apr 01 04:00:00 EST 1986

DOI:https://doi.org/10.2172/7104107· OSTI ID:7104107

Bern, Z

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., CA (USA); California Univ., Berkeley (USA). Dept. of Physics
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 7104107
• Report Number(s): LBL-22303; ON: DE87002549
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACTION INTEGRAL
ELECTRODYNAMICS
ELEMENTARY PARTICLES
EQUATIONS
FIELD THEORIES
GAUGE INVARIANCE
GLUONS
INTEGRALS
INVARIANCE PRINCIPLES
LANGEVIN EQUATION
LORENTZ INVARIANCE
MASS
POSTULATED PARTICLES
QUANTIZATION
QUANTUM FIELD THEORY
REST MASS
STOCHASTIC PROCESSES