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.