Gauge-fixing degeneracies and confinement in non-Abelian gauge theories

Journal Article · Wed Feb 15 04:00:00 EST 1978 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.17.1086· OSTI ID:7075197

Bender, C M; Eguchi, T; Pagels, H

Following several suggestions of Gribov we have examined the problem of gauge-fixing degeneracies in non-Abelian gauge theories. First we modify the usual Faddeev-Popov prescription to take gauge-fixing degeneracies into account. We obtain a formal expression for the generating functional which is invariant under finite gauge transformations and which counts gauge-equivalent orbits only once. Next we examine the instantaneous Coulomb interaction in the canonical formalism with the Coulomb-gauge condition. We find that the spectrum of the Coulomb Green's function in an external monopole-like field configuration has an accumulation of negative-energy bound states at E = 0. Using semiclassical methods we show that this accumulation phenomenon, which is closely linked with gauge-fixing degeneracies, modifies the usual Coulomb propagator form vertical-barkvertical-bar/sup -2/ to vertical-barkvertical-bar/sup -4/ for small vertical-barkvertical-bar. This confinement behavior depends only on the long-range behavior of the field configuration. We thereby demonstrate the conjectured confinement property of non-Abelian gauge theories in the Coulomb gauge.

• Research Organization: Department of Physics, Washington University, St. Louis, Missouri 63130
• OSTI ID: 7075197
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 17:4; ISSN PRVDA
• Country of Publication: United States
• Language: English

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
BOUND STATE
COULOMB FIELD
ELECTRIC FIELDS
FUNCTIONS
GAUGE INVARIANCE
GREEN FUNCTION
HAMILTONIANS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL OPERATORS
PROPAGATOR
QUANTUM OPERATORS
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS