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

J. Math. Phys. 62, 071701 (2021) 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 perfo...

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Bibliographic Details
Main Authors Choreño, E, Valencia, R, Ojeda-Guillén, D
Format Journal Article
LanguageEnglish
Published 30.08.2020
Subjects
Mathematics - Mathematical Physics
Physics - Mathematical Physics
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Summary:J. Math. Phys. 62, 071701 (2021) 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.
DOI:10.48550/arxiv.2008.13271