Quantization of spinor fields. II. Meaning of ''bosonization'' in 1+1 and 1+3 dimensions

We demonstrate that the correspondence principle allowing us to relate the classical (c number) and quantum levels of spinor fields in 1+1 and 1+3 dimensions, involves free Bose systems with unbounded from below Hamiltonians. The necessary condition for the quantum spinor fields to be ''bosonized'' on the ''physical'' space is that for the related free Bose systems, only the non-negative part of the spectrum persists, due to constraints. Compared with the bosonization formulas, the number of independent Bose degrees of freedom necessary for a consistent formulation of the correspondence principle is doubled