The q-analogue of the Higgs algebra
https://doi.org/10.29235/1561-2430-2021-57-4-447-454
Abstract
In this paper, the q-generalization of the Higgs algebra is considered. The realization of this algebra is shown in an explicit form using a nonlinear transformation of the creation-annihilation operators of the q-harmonic oscillator. This transformation is the performance of two operations, namely, a “correction” using a function of the original Hamiltonian, and raising to the fourth power the creation and annihilation operators of a q-harmonic oscillator. The choice of the “correcting” function is justified by the standard form of commutation relations for the operators of the metaplectic realization Uq(SU(1,1)). Further possible directions of research are briefly discussed to summarize the results obtained. The first direction is quite obvious. It is the consideration of the problem when the dimension of the operator space increases or for any value N. The second direction can be associated with the analysis of the relationship between q-generalizations of the Higgs and Hahn algebras.
About the Authors
A. N. Lavrenov
Belarusian State Pedagogical University
Belarus
Belarus
Alexandre N. Lavrenov – Ph. D. (Physics and Mathematics), Associate Professor, Associate Professor of the Department of the Chair of Information Technologies in Education
18, Sovetskaya Str., 220050
I. A. Lavrenov
Octonion technology Ltd.
Belarus
Belarus
Ivan A. Lavrenov – Leading Specialist
25, Ya. Kupala Str., 220030, Minsk
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