On the Uniqueness of the Fock Quantization of the Dirac Field in the Closed FRW Cosmology

TL;DR

This paper investigates whether the Fock quantization of the Dirac field in a closed FRW cosmology is unique, extending methods used for scalar fields to address ambiguities in quantum field representation in curved spacetime.

Contribution

It demonstrates the conditions under which the Fock quantization of the Dirac field in closed FRW spacetime is unique, using criteria of unitary dynamics similar to scalar field cases.

Findings

Fock quantization of the Dirac field is unique under certain conditions.

The criteria used effectively remove quantization ambiguities.

Results extend previous scalar field analyses to fermionic fields.

Abstract

The Fock quantization of free fields propagating in cosmological backgrounds is in general not unambiguously defined due to the non-stationarity of the spacetime. For the case of a scalar field in cosmological scenarios it is known that the criterion of unitary implementation of the dynamics serves to remove the ambiguity in the choice of Fock representation (up to unitary equivalence). Here, applying the same type of arguments and methods previously used for the scalar field case, we discuss the issue of the uniqueness of the Fock quantization of the Dirac field in the closed FRW spacetime proposed by D'Eath and Halliwell.