On the Wavefunctional for Two Heavy Color Sources in Yang-Mills Theory

TL;DR

This paper develops a method to identify the correct wavefunctionals for heavy color sources in nonabelian Yang-Mills theory, emphasizing the importance of separating gauge-invariant degrees of freedom and respecting the center symmetry Z_N.

Contribution

It introduces a systematic approach to distinguish gauge-invariant states and wavefunctionals in nonabelian gauge theories, extending ideas from abelian theories to SU(N).

Findings

Proper separation of gauge degrees of freedom is achieved.

Wavefunctionals consistent with Z_N center symmetry are constructed.

The approach clarifies the structure of the Hilbert space for heavy sources.

Abstract

In an abelian gauge theory, the Coulombic potential between two static charges is obtained most directly when a correct separation between gauge-invariant and gauge degrees of freedom is made. This motivates a similar separation in the nonabelian theory. When a careful identification of the Hilbert space is made, along with the proper analyticity requirements, it is then possible to find the appropriate wavefunctionals describing heavy color sources in the theory. This treatment is consistent with, and realizes in a simple way the center symmetry Z_N of SU(N) gauge theories.