Boson--Fermion hybrid representation formulation, I

A boson--fermion hybrid representation is presented. In this framework, a fermion system is described concurrently by the bosonic and the fermonic degrees of freedom. A fermion pair in this representation can be treated as a boson without violating the Pauli principle. Furthermore the ''bosonic interactions'' are shown to originate from the exchange processes of the fermions and can be calculated from the original fermion interactions. Both the formulation of the BFH representations for the even and odd nuclear systems are given. We find that the basic equation of the nuclear field theory (NFT) is just the usual Schroedinger equation in such a representation with the empirical NFT diagrammatic rules emerging naturally. This theory was numerically checked in the case of four nucleons moving in a single-j shell and the exactness of the theory was established