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arXiv · 2005.09500

New BCH-like relations of the su(1, 1), su(2) and so(2, 1) Lie algebras

D. M. Tibaduiza·A. H. Aragão·C. Farina·C. A. D. Zarro
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Abstract

In this work we demonstrate new BCH-like relations involving the generators of the su(1, 1), su(2) and so(2, 1) Lie algebras. We use our results to obtain in a straightforward way the composition of an arbitrary number of elements of the corresponding Lie groups. In order to make a self-consistent check of our results, as a first application we recover the non-trivial composition law of two arbitrary squeezing operators. As a second application, we show how our results can be used to compute the time evolution operator of physical systems described by time-dependent hamiltonians given by linear combinations of the generators of the aforementioned Lie algebras.

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D. M. Tibaduiza, A. H. Aragão, C. Farina, C. A. D. Zarro. 2020-05-19. New BCH-like relations of the su(1, 1), su(2) and so(2, 1) Lie algebras. https://doi.org/10.1016/j.physleta.2020.126937

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