Lorentz gauge quantization in synchronous coordinates

TL;DR

This paper extends the application of Dirac's quantization method to impose the Lorentz gauge in general space-times expressed in synchronous coordinates, overcoming limitations of previous approaches in non-static backgrounds.

Contribution

It generalizes the Dirac quantization approach for the Lorentz gauge to arbitrary space-times in synchronous coordinates, broadening its applicability.

Findings

Dirac's method successfully imposes the Lorentz gauge in general synchronous coordinate space-times.

The approach overcomes limitations of the Gupta-Bleuler method in non-static backgrounds.

The results facilitate quantization in more general gravitational settings.

Abstract

It has been shown that the Gupta-Bleuler method of quantization can be used to impose the Lorentz gauge condition in static space-times but not in cosmological space-times. This implies that the Gupta-Bleuler approach fails in general in non-static space-times. More recently, however, the Dirac method of quantizing constrained dynamical systems has been successfully employed to impose the Lorentz gauge in conformally flat space-times. In this paper we generalize this result by using Dirac's method to impose the Lorentz gauge in a general space-time region where the metric is expressed in synchronous coordinates.