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Communications in Theoretical Physics

Analytic Calculation of Arbitrary Matrix Elements for Boson Exponential Quadratic Operators

Pan Jianwei, Hou Guang, Zhang Yongde

Published Jun 15, 1998• 1 citation
Publisher

Abstract

By means of the transformation relation between the ordinary form of boson exponential quadratic operators (BEQO) and its anti-normal product form, we present an effective method to conveniently calculate arbitrary matrix elements of BEQO. By this method, many important matrix elements can be calculated analytically. As a direct application, we obtain the exact solutions of the density matrix and partition function for general boson quadratic Hamiltonian without any information about the energy level.

DOI
10.1088/0253-6102/29/4/547

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By means of the transformation relation between the ordinary form of boson exponential quadratic operators (BEQO) and its anti-normal product form, we present an effective method to conveniently calculate arbitrary matrix elements of BEQO. By this method, many important matrix elements can be calculated analytically. As a direct application, we obtain the exact solutions of the density matrix and partition function for general boson quadratic Hamiltonian without any information about the energy level.
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In this paper, we studied the general formula of normal product calculation for boson exponential quadratic operators (EQO) which is first obtained by WANG et al. (J. Phys. A: Math. Gen. 27 (1994) 6563]. It is shown that the boundness of boson EQO will result in a restriction on the applicable bounds of this formula. According to the restriction condition, the conclusion about unity operator given by MA et al. [Commun. Theor. Phys. (Beijing,China) 21 (1994) 119] should be made some corresponding corrections. At last, we extended this formula to the case of fermion for the convenience of later applications.