Schwinger-Dyson equations in Coulomb gauge consistent with numerical simulation

In the present work, we undertake a study of the Schwinger-Dyson equation (SDE) in the Euclidean formulation of local quantum gauge field theory, with Coulomb gauge condition partial derivative(i)A(i) = 0. We continue a previous study which kept only instantaneous terms in the SDE that are proportional to delta(t) in order to calculate the instantaneous part of the time component of the gluon propagator D-A0A0 (t, R). We compare the results of that study with a numerical simulation of lattice gauge theory and find that the infrared critical exponents and related quantities agree to within 1% to 3%. This raises the question, "Why is the agreement so good, despite the systematic neglect of noninstantaneous terms?" We discovered the happy circumstance that all the noninstantaneous terms are in fact zero. They are forbidden by the symmetry of the local action in Coulomb gauge under time-dependent gauge transformations g(t). This remnant gauge symmetry is not fixed by the Coulomb gauge condition. The numerical result of the present calculation is the same as in the previous study; the novelty is that we now demonstrate that all the non-instantaneous terms in the SDE vanish. We derive some elementary properties of propagators which are a consequence of the remnant gauge symmetry. Our results support the simple physical scenario in which confinement is the result of a linearly rising color-Coulomb potential, V(R) similar to sigma R at large R. We also show that the horizon condition < H(gA)> = (N-2-1)dV, and the divergence of the ghost dressing function at k = 0, lim(vertical bar k -> 0 vertical bar)k(2)D(c (c) over bar)(k) = infinity, are identical gauge conditions.