Quantum Field Theory of Fermions and Parafermions Constructed from Quantum Bose Fields. I: Simplification and Generalization

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Abstract
In previous papers a Bose representation of fermions and parafermions was constructed in such a way that (1) the only fundamental quantum fields were Bose fields and (2) no property of the Fermi or para-Fermi systems (as e.g., the Pauli principle for fermions) be lost. The use of that construction and also the proofs of the theorems were made difficult by the complexity of many of the mathematical expressions we used previously. In the present paper we simplify much the above-mentioned construction. Moreover no results (concerning the Bose representation) proved in the previous papers are lost in the present reformulation, but all results are more general: In the previous papers we made the construction of the Bose representation of fermions for the case of pure Fock representations of Quantum Field Theory. The present work is consistent with Fock as well as with non-Fock representations of the Fermi anticommutation relations.

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