ar X iv : h ep - l at / 0 40 70 22 v 1 1 3 Ju l 2 00 4 Remnant Symmetry and the Confinement Phase in Coulomb Gauge ∗

The color Coulomb potential is derived from the expectation value of the non-local part of the Coulomb-gauge Hamiltonian, in the presence of static external charges. This is a 1/R potential in electrodynamics, but the R-dependence may be different in non-abelian gauge theories. In this talk I will show that the confining behavior of the color Coulomb potential depends on the unbroken realization of a global gauge symmetry, which remains after imposing Coulomb gauge. I will also make some connections to the vortex confinement mechanism, and this theme will be further developed in Dan Zwanziger’s talk. The results outlined here are reported in much greater detail in ref. [1]; I will also touch on the studies in refs. [2] and [3]. Let |Ψqq〉 = q(0)q(R)|Ψ0〉 denote a physical state in Coulomb gauge containing heavy quarkantiquark static charges, where Ψ0 is the YangMills vacuum wavefunctional. Then