Nonlocal regularizations of gauge theories

Journal Article · Tue Jan 15 04:00:00 EST 1991 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.43.499· OSTI ID:6150935

Evens, D; Moffat, J W ^[1]; Kleppe, G; Woodard, R P ^[2]

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1. Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7 (CA)
2. Department of Physics, University of Florida, Gainesville, Florida 32611 (USA)

A procedure is given for generalizing local, gauge-invariant field theories to nonlocal ones which are finite, Poincare invariant, and perturbatively unitary. These theories are endowed with nonlocal gauge symmetries which ensure current conservation and decoupling in the same way that their local analogs do in the parent theories. An elegant way of viewing the resulting on-shell symmetry transformations is as quantum representations'' of the local gauge group in which the representation matrices become field-dependent, nonlocal operators. By varying the scale of nonlocality one can obtain gauge-invariant regularization schemes which are manifestly Poincare invariant, perturbatively unitary, and free of automatic subtractions. Since our method does not entail changing either the particle content or the dimension of spacetime, it may preserve global supersymmetry. As applications we work out the electron self-energy and vacuum polarization in QED at one loop. The latter gives the surprising result that no Landau ghost occurs with the regulator on and before renormalization. Another surprise is the absence of an axial-vector anomaly.

• DOE Contract Number: FG05-86ER40272
• OSTI ID: 6150935
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 43:2; ISSN 0556-2821; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645300 -- High Energy Physics-- Particle Invariance Principles & Symmetries
645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMPOSITE MODELS
COUPLING CONSTANTS
ELECTRODYNAMICS
ELECTRONS
ELEMENTARY PARTICLES
ENERGY
EXTENDED PARTICLE MODEL
FERMIONS
FIELD THEORIES
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LEPTONS
LIE GROUPS
LORENTZ INVARIANCE
MATHEMATICAL MODELS
MATRICES
NONLOCAL POTENTIAL
PARTICLE MODELS
PERTURBATION THEORY
POINCARE GROUPS
POTENTIALS
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
QUARK MODEL
RENORMALIZATION
S MATRIX
SELF-ENERGY
SPACE-TIME
STRING MODELS
SUPERSYMMETRY
SYMMETRY
SYMMETRY GROUPS
ULTRAVIOLET DIVERGENCES
VACUUM POLARIZATION