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借助线性量子变换(LQT)理论,对n模玻色和费米子的二次型哈密顿量,我们给出了简洁的对角化形式.并且指出,对于n模玻色子耦合二次型哈密顿量,通过一个负幺正矩阵(它是复辛群SP(2n,c)的元素)可以把它对角化;对n模费米子耦合二次型哈密顿量,通过一个幺正矩阵(它是复费米群F(2n,c)的元素)可以把它对角化.

参考文献

[1] Bogoliubov N N, Bogoliubov N N Jr. Introduction to Quantum Statistics [M]. (Chinese version), 1994.
[2] Blaizot J P. Quantum Theory of Finite Systems [M]. Massachusetts: MIT Press, 1986.
[3] Zhang Yongde, Tang Zhong. General theory of linear quantum transformation in Bargmarm-Fock space [J]. Nuovo Cimento. B, 1994, 109:387
[4] Zhang Yongde, Tang Zhong. Quantum transformation theory on Fermion Fock space [J]. J. Math. Phys., 1993,34:5639
[5] Wang Xiangbin, Yu Sixia, Zhang Yongde. Linear quantum transformation and normal product calculation of Boson exponential quadratic operators [J]. J. Phys. A. Math. Gen., 1994, 27:6563
[6] Pan Jianwei, Zhang Yongde, Wang Xiangbin et al. Some addenda about the general formula of normal product calculation for Boson exponential quadratic operators [J]. Commun. Theor. Phys., 1996, 26:479
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