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

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