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

TL;DR

This paper investigates the static force potential between sources in non-abelian gauge theory within a finite periodic or twisted box, analyzing perturbative behavior and the effects of boundary conditions in Coulomb gauge.

Contribution

It provides a detailed perturbative analysis of the force potential in non-abelian gauge theory at finite volume, including effects of twist and boundary conditions.

Findings

Confirmation of the change in effective coupling at one-loop order.

Derivation of the Coulomb Green function convolution for potential.

Analysis of twist effects on the Green function.

Abstract

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 non-singular at $\bm{x}=\bm{y}$. The effect of the twist comes in through its Green function of the sector.