Static force potential of a non-Abelian gauge theory in a finite box in Coulomb gauge

Force potential exerting between two classical static sources of pure non-Abelian gauge theory in the Coulomb gauge is reconsidered at a periodic/twisted box of size L-3. Its perturbative behavior is examined by the short-distance expansion as well as by the derivative expansion. The latter expansion to one-loop order confirms the well-known change in the effective coupling constant at the Coulomb part as well as the Uehling potential while the former is given by the convolution of two Coulomb Green functions being nonsingular at x = y. The effect of the twist comes in through its Green function of the sector.

Automated summary

This article revisited the force potential exerting between two classical static sources of pure non-Abelian gauge theory in the Coulomb gauge, examining its perturbative behavior through short-distance expansion and derivative expansion. The latter expansion confirmed the well-known change in effective coupling constant in the Coulomb part as well as the Uehling potential, while the former involved the convolution of two Coulomb Green functions which were non-singular at x = y. The effect of the twist was introduced through the Green function of the sector.