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A major problem in the quantization of fields in curved spacetimes is theambiguity in the choice of a Fock representation for the canonical commutationrelations. There exists an infinite number of choices leading to differentphysical predictions. In stationary scenarios, a common strategy is to select avacuum (or a family of unitarily equivalent vacua) by requiring invarianceunder the spacetime symmetries. When stationarity is lost, a naturalgeneralization consists in replacing time invariance by unitarity in theevolution. We prove that, when the spatial sections are compact, the criterionof a unitary dynamics, together with the invariance under the spatialisometries, suffices to select a unique family of Fock quantizations for ascalar field with time dependent mass.

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