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.

By the aid of the linear quantum transformation (LQT) theory,we give a concise diagonalization for n-mode boson and fermion of quadratic Hamiltonian. It is also pointed out that an n-mode boson coupled quadratic Hamiltonian can be diagonalized by a "negative unitary" matrix which is an element of complex symplectic group SP(2n,c),and an n-mode fermion coupled quadratic Hamiltonian can be diagonalized by a unitary matrix which is an element of complex fermion group F(2n,c).