Algebraic approach and Berry phase of a Hamiltonian with a general SU(1, 1) symmetry

In this paper we study a general Hamiltonian with a linear structure given in terms of two different realizations of the $SU(1,1)$ group. We diagonalize this Hamiltonian by using the similarity transformations of the $SU(1,1)$ and $SU(2)$ displacement operators performed to the $su(1,1)$ Lie algebra generators. Then, we compute the Berry phase of a general time-dependent Hamiltonian with this general $SU(1,1)$ linear structure.