Gauge degrees of freedom, external charges, and quark confinement criterion in theA0=0canonical formalism

Abstract

The ${A}_{0}=0$ canonical formalism is shown to be completely consistent even though Gauss's law is not verified as a field equation. This is so because the Hilbert space of states must also involve states coupled with external static charge distributions. Indeed these cannot be handled by adding the standard ${A}_{\ensuremath{\mu}}{j}_{\ensuremath{\mu}}^{\mathrm{ext}}$term because it vanishes identically in the ${A}_{0}=0$ gauge for static charges. The corresponding charge densities are instead the eigenvalues of the operator of infinitesimal time-independent gauge transformations which commute with the Hamiltonian. The implications of this viewpoint are discussed in connection with Gribov's phenomenon, the $\ensuremath{\theta}$ vacuum, perturbation theory, and quark confinement. The constant of motion due to gauge invariance in gauge theories plays the same role as the constant of motion due to translational invariance in soliton quantization.