Gauge-fixing degeneracies and confinement in non-Abelian gauge theories
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), Vol. 17:4
- Country of Publication:
- United States
- Language:
- English
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GAUGE INVARIANCE
COULOMB FIELD
BOUND STATE
GREEN FUNCTION
HAMILTONIANS
PROPAGATOR
SU-2 GROUPS
ELECTRIC FIELDS
FUNCTIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
SU GROUPS
SYMMETRY GROUPS
645201* - High Energy Physics- Particle Interactions & Properties-Theoretical- General & Scattering Theory
645400 - High Energy Physics- Field Theory