Lorenz gauge quantization in conformally flat spacetimes

TL;DR

This paper extends Lorenz gauge quantization using Dirac's method to general conformally flat spacetimes, demonstrating no particle production in four dimensions but particle creation in other dimensions during scale factor changes.

Contribution

It generalizes Lorenz gauge quantization via Dirac's method to conformally flat spacetimes and analyzes particle production across different dimensions.

Findings

No particle production in 4D conformally flat spacetimes.

Particle production occurs in D≠4 when the scale factor changes.

Particle production due to sudden scale factor change calculated.

Abstract

Recently it was shown that Dirac's method of quantizing constrained dynamical systems can be used to impose the Lorenz gauge condition in a four-dimensional cosmological spacetime. In this paper we use Dirac's method to impose the Lorenz gauge condition in a general four-dimensional conformally flat spacetime and find that there is no particle production. We show that in cosmological spacetimes with dimension $D\neq 4$ there will be particle production when the scale factor changes, and we calculate the particle production due to a sudden change.