New York University
I report on a study of the Schwinger-Dyson equation (SDE) in the Euclidean formulation of local quantum gauge field theory, with Coulomb gauge condition ∂iAi = 0. 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 is so good, despite the systematic neglect of non-instantaneous terms? We discovered the happy circumstance that all the non-instantaneous 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 a 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. In particular the time component of the gluon propagator is found to be purely instantaneous DA0A0 (t, R) = δ(t)V (R), where V (R) is the color-Coulomb potential. There is no non-instantaneous part. Our results support the simple physical scenario in which confinement is the result of a linearly rising color-Coulomb potential, V (R) ∼ σR at large R.