Instantaneous Coulomb interaction in quantum chromodynamics

The instantaneous Coulomb interaction is studied in the SU(2) Yang-Mills theory. The Coulomb Green's function and quark-antiquark static potential are evaluated in a background gauge field that is spherically symmetric and of short range. Expansion of the Coulomb Green's function in vector spherical harmonic functions reduces the problem to a radial problem. The radial problem can be solved if the background field is taken to be sharply cut off at a range $\rho$. Translation invariance is restored by averaging the potential over superpositions of the background field in the dilute-gas approximation. The resulting potential $V\left(R\right)\mathrm{}$ is asymptotically proportional to $R^{-1\mathrm{}}$. The strength of the potential is examined as a function of the magnitude of the background field. It is argued that instantons produce vacuum fluctuations similar to the background field that is used here.