Dirac fields in flat FLRW cosmology: Uniqueness of the Fock quantization

TL;DR

This paper establishes a unique Fock quantization for Dirac fields in flat FLRW cosmology by imposing symmetry invariance and unitarity of quantum dynamics, resolving ambiguity in vacuum selection.

Contribution

It proves the uniqueness of the Fock vacuum for Dirac fields in flat FLRW spacetime under specific physical conditions, regardless of spin structure choices.

Findings

Uniqueness of Fock quantization is guaranteed under symmetry and unitarity conditions.

Explicit characterization of the unitarily implementable part of the Dirac dynamics.

Identification of a physically motivated convention for particles and antiparticles.

Abstract

We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed.