QUANTUM TRANSFORMATION THEORY IN FERMION FOCK SPACE

In this article a general linear quantum transformation U for the foll owing fermion system with n modes, (b'+,b') = U(b+,b) U-1 = (b+,b) (A, /B, D/C), is studied. All above transformations in Fock space are prov ed to form a ray representation of a group which is isomorphic with O( 2n,C). The explicit expressions of operator U in terms of the normal o rdered product and non-normal ordered product are obtained. A series o f auxiliary identities are given. It has been mentioned that the resul ts are applicable to the case of fermion fields with interaction.