A uniqueness criterion for the Fock quantization of scalar fields with time dependent mass

TL;DR

This paper establishes a criterion combining unitarity of evolution and spatial symmetry invariance to uniquely determine the Fock quantization of scalar fields with time-dependent mass in compact spacetimes.

Contribution

It proves that in compact spatial sections, the combined conditions of unitarity and symmetry invariance uniquely specify the Fock quantization, resolving ambiguity issues.

Findings

Uniqueness of Fock quantization under specified conditions

Conditions applicable to scalar fields with time-dependent mass

Applicable to compact spatial sections

Abstract

A major problem in the quantization of fields in curved spacetimes is the ambiguity in the choice of a Fock representation for the canonical commutation relations. There exists an infinite number of choices leading to different physical predictions. In stationary scenarios, a common strategy is to select a vacuum (or a family of unitarily equivalent vacua) by requiring invariance under the spacetime symmetries. When stationarity is lost, a natural generalization consists in replacing time invariance by unitarity in the evolution. We prove that, when the spatial sections are compact, the criterion of a unitary dynamics, together with the invariance under the spatial isometries, suffices to select a unique family of Fock quantizations for a scalar field with time dependent mass.