QUANTUM TRANSFORMATION THEORY IN FERMION FOCK SPACE

In this article a general linear quantum transformation U for the following 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 proved 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 ordered product and non-normal ordered product are obtained. A series of auxiliary identities are given. It has been mentioned that the results are applicable to the case of fermion fields with interaction.