On the Yang-Mills wave functional in Coulomb gauge

TL;DR

This paper studies the Yang-Mills wave functional in Coulomb gauge, revealing that its infrared behavior is robust and determined by the Faddeev-Popov determinant's divergence at the Gribov horizon, independent of certain variational details.

Contribution

It demonstrates that, within a one-loop resummation, the vacuum energy is unaffected by the Faddeev-Popov determinant's power and the wave functional becomes field-independent in the infrared.

Findings

Infrared wave functional becomes field-independent, indicating a stochastic vacuum.

Vacuum energy is independent of the Faddeev-Popov determinant's power within one-loop resummation.

Infrared behavior is governed solely by the divergence at the Gribov horizon.

Abstract

We investigate the dependence of the Yang-Mills wave functional in Coulomb gauge on the Faddeev-Popov determinant. We use a Gaussian wave functional multiplied by an arbitrary power of the Faddeev-Popov determinant. We show, that within the resummation of one-loop diagrams the stationary vacuum energy is independent of the power of the Faddeev-Popov determinant and, furthermore, the wave functional becomes field-independent in the infrared, describing a stochastic vacuum. Our investigations show, that the infrared limit is rather robust against details of the variational ans\"atze for the Yang-Mills wave functional. The infrared limit is exclusively determined by the divergence of the Faddeev-Popov determinant at the Gribov horizon.