Renormalizable Non-Covariant Gauges and Coulomb Gauge Limit

TL;DR

This paper introduces interpolating gauges between covariant and physical gauges, demonstrating their renormalizability and analyzing the Coulomb gauge limit, revealing finite correlation functions and invariance properties of certain fields.

Contribution

It extends the BRST method to include Lorentz symmetry, proving the renormalizability of interpolating gauges and analyzing the Coulomb gauge as a singular limit.

Findings

Interpolating gauges are renormalizable.

Correlation functions remain finite in the Coulomb limit.

The field component gA_0 is invariant under renormalization.

Abstract

To study ``physical'' gauges such as the Coulomb, light-cone, axial or temporal gauge, we consider ``interpolating'' gauges which interpolate linearly between a covariant gauge, such as the Feynman or Landau gauge, and a physical gauge. Lorentz breaking by the gauge-fixing term of interpolating gauges is controlled by extending the BRST method to include not only the local gauge group, but also the global Lorentz group. We enumerate the possible divergences of interpolating gauges, and show that they are renormalizable, and we show that the expectation value of physical observables is the same as in a covariant gauge. In the second part of the article we study the Coulomb-gauge as the singular limit of the Landau-Coulomb interpolating gauge. We find that unrenormalized and renormalized correlation functions are finite in this limit. We also find that there are finite two-loop diagrams of ``unphysical'' particles that are not present in formal canonical quantization in the Coulomb gauge. We verify that in the same limit, the Gauss-BRST Ward identity holds, which is the functional analog of the operator statement that a BRST transformation is generated by the Gauss-BRST charge. As a consequence, $gA_0$ is invariant under renormalization, whereas in a covariant gauge, no component of the gluon field has this property.