Temporal Wilson loop in the Hamiltonian approach in Coulomb gauge

TL;DR

This paper explores the temporal Wilson loop in Yang-Mills theory using the Hamiltonian approach in Coulomb gauge, deriving known results in simple cases and approximating the Wilson loop in realistic (3+1) dimensions, finding agreement between Wilson and Coulomb string tensions.

Contribution

It applies the Coulomb gauge Hamiltonian approach to compute the temporal Wilson loop in (3+1) dimensions, demonstrating the consistency of Wilson and Coulomb string tensions within an approximation scheme.

Findings

Wilson and Coulomb string tensions agree in (3+1)D Yang-Mills theory within the approximation

Exact solutions are derived for simple cases like Abelian and (1+1)D non-Abelian theories

The approach can incorporate approximate vacuum wave functionals for realistic theories

Abstract

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be derived using unitary transformations to take care of time evolution. Alternatively, the exact solution can also be found in Coulomb gauge using the exact ground state wave functional which is known explicitly in these simple cases. The Coulomb gauge technique can also be applied to the more realistic case of Yang-Mills theory in (3+1) dimensions, where one has to rely on the approximate vacuum wave functional obtained e.g. in recent variational approaches. We use this formulation to compute the temporal Wilson loop in (3+1) dimensional Yang-Mills theory, and find that the Wilson and Coulomb string tension agree within this approximation scheme. Possible improvements of these findings are briefly discussed.