Unique Fock quantization of a massive fermion field in a cosmological scenario

TL;DR

This paper establishes a unique Fock quantization for a massive Dirac field in a cosmological setting with spherical spatial sections, ensuring invariance under symmetries and unitary evolution, thus resolving quantization ambiguities.

Contribution

It proves the uniqueness (up to unitary equivalence) of Fock quantizations for a massive fermion in a cosmological background under symmetry and unitarity conditions.

Findings

Identifies a unique class of Fock representations satisfying the imposed conditions.

Demonstrates unitary equivalence of these representations under mild background variations.

Provides a complete characterization of physically reasonable fermion quantizations.

Abstract

It is well known that the Fock quantization of field theories in general spacetimes suffers from an infinite ambiguity, owing to the inequivalent possibilities in the selection of a representation of the canonical commutation or anticommutation relations, but also owing to the freedom in the choice of variables to describe the field among all those related by linear time-dependent transformations, including the dependence through functions of the background. In this work we remove this ambiguity (up to unitary equivalence) in the case of a massive Dirac free field propagating in a spacetime with homogeneous and isotropic spatial sections of spherical topology. Two physically reasonable conditions are imposed in order to arrive to this result: (a) The invariance of the vacuum under the spatial isometries of the background, and (b) the unitary implementability of the dynamical evolution that dictates the Dirac equation. We characterize the Fock quantizations with a non trivial fermion dynamics that satisfy these two conditions. Then, we provide a complete proof of the unitary equivalence of the representations in this class under very mild requirements on the time variation of the background, once a criterion to discern between particles and antiparticles has been set.