The partition function versus boundary conditions and confinement in the Yang-Mills theory

TL;DR

This paper investigates how boundary conditions influence the partition function in gauge theories, revealing that in non-Abelian gluodynamics, certain boundary conditions induce confinement phenomena at low temperatures.

Contribution

It demonstrates the impact of boundary conditions on the partition function and confinement in SU(2) gauge theories, extending understanding beyond Abelian cases.

Findings

In Abelian theory, only slowly decreasing charge distributions affect the partition function.

In SU(2) gluodynamics, below a critical temperature, the partition function depends sharply on boundary conditions.

This dependence leads to color confinement at low temperatures.

Abstract

We analyse dependence of the partition function on the boundary condition for the longitudinal component of the electric field strength in gauge field theories. In a physical gauge the Gauss law constraint may be resolved explicitly expressing this component via an integral of the physical transversal variables. In particular, we study quantum electrodynamics with an external charge and SU(2) gluodynamics. We find that only a charge distribution slowly decreasing at spatial infinity can produce a nontrivial dependence in the Abelian theory. However, in gluodynamics for temperatures below some critical value the partition function acquires a delta-function like dependence on the boundary condition, which leads to colour confinement.