Quantum transformation theory in fermion Fock space
Yong-de Zhang, Zhong Feng Tang
In this article a general linear quantum transformation U for the following fermion system with n modes, (b′+,b̃′)=U(b+,b̃)U−1=(b+,b̃)(B̃, A, C̃D), 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.
Journal of Mathematical Physics•Dec 1, 1993•21 citations