Quantum Fields in an Expanding Universe

TL;DR

This paper investigates quantum fields in an expanding universe, analyzing scalar, electromagnetic, and Dirac fields, focusing on conformal invariance and particle production effects within a Robertson-Walker metric.

Contribution

It extends previous scalar field analysis to electromagnetic and Dirac fields using invariants, clarifying conformal invariance properties and their impact on particle production.

Findings

Electromagnetic and massless spinor actions are conformally invariant.

Massless conformally coupled scalar field is not conformally invariant.

Surface terms cause conformal symmetry violation affecting quantized theory.

Abstract

We extend our analysis for scalar fields in a Robertson-Walker metric to the electromagnetic field and Dirac fields by the method of invariants. The issue of the relation between conformal properties and particle production is re-examined and it is verified that the electromagnetic and massless spinor actions are conformal invariant, while the massless conformally coupled scalar field is not. For the scalar field case it is pointed out that the violation of conformal simmetry due to surface terms, although ininfluential for the equation of motion, does lead to effects in the quantized theory.