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

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.

7 pages

References in corpus (1)

• A time-dependent harmonic oscillator with two frequency jumps: an exact algebraic solution

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