Quantization of spinor fields

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Abstract
Influenced by Klauder’s investigations on the same subject, we study the question of correspondence principle for Dirac fields, looking for its formulation without use of Grassman algebras. We prove that with each Fermi operator (the series with respect to asymptotic free fields): Ω (ψ,ψ̄): one can associate the functional ΩC(ψC, ψ̄C) with respect to classical spinor fields. Here the projector 1F and the Hilbert (Fock) space FF=1FFB are given such that the identity 1F: ΩC(ψB, ψ̄B): 1FFF = :Ω (ψ, ψ̄):FF defines the mediating boson level, where coherent state expectation values of operator expressions are in order: 〈:ΩC(ψB, ψ̄B):〉=ΩC(ψC, ψ̄C). For proofs we employ functional differentiation (resp. integration) methods, especially in connection with the use of functional representations of the CCR and CAR algebras.