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Communications in Theoretical Physics

Linear Quantum Transform Theory in Bargmann–Fock Space and Its Preliminary Application

Yong-De Zhang, Zhong Feng Tang

Published Jan 30, 1995• 5 citations
Publisher

Abstract

A general theory for the linear transform in Bargmann–Fock space of n-mode boson system is presented. The group structure of transform is analyzed and the explicit expressions of transform operations in terms of normal ordering are given. As applications, a series of useful identities are given, the decoupling problem for general two-boson interaction and the normal product calculation of boson exponential quadratic operators are studied.

DOI
10.1088/0253-6102/23/1/57

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A general theory for the linear transform in Bargmann–Fock space of n-mode boson system is presented. The group structure of transform is analyzed and the explicit expressions of transform operations in terms of normal ordering are given. As applications, a series of useful identities are given, the decoupling problem for general two-boson interaction and the normal product calculation of boson exponential quadratic operators are studied.
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.