Analytic calculation of color-Coulomb potential and color confinement

Abstract

We develop a calculational scheme in Coulomb and temporal gauge that respects gauge invariance and is most easily applied to the infrared asymptotic region of QCD. It resembles the Dyson-Schwinger equations of Euclidean quantum field theory in Landau gauge, but is 3-dimensional. A simple calculation yields a color-Coulomb potential that behaves at large $R$ approximately like $V_{\mathrm{coul}}(R)\sim R^{[1-0.2(d-1)]}$ for spatial dimension $1\le d\le 3$. This is a linearly rising potential plus a rather weak dependence on $d$.

Comments: 12 pages