Perturbative Yang-Mills Ground State in the Temporal Gauge

TL;DR

This paper computes second order corrections to the ground state and vacuum energy of Yang-Mills theory in the temporal gauge, highlighting renormalization and the running coupling in a gauge-invariant framework.

Contribution

It introduces a gauge-invariant approach to renormalization and the running coupling in the temporal gauge for Yang-Mills theory, connecting to axial gauge results.

Findings

Renormalization constants match those of the Axial gauge.

Dimensional regularization effectively handles divergences.

Ground state energy receives specific second order corrections.

Abstract

Second order corrections to the perturbative ground state wave functional and vacuum energy of a Yang-Mills theory are calculated in the temporal gauge. Using dimensional regularization, the concepts of renormalization and a running coupling constant are motivated in a spatially gauge invariant way, before the introduction of a scalar product. After definition of a scalar product, it is shown that the renormalization constants of this approach are just those of the Axial gauge.