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Deformed oscillators and their applications. (Russian. English summary) Zbl 0744.17010

This is a short review of papers on \(q\)-deformed oscillators and on their applications. The authors show that \(q\)-oscillators are natural from the point of view of contractions of quantum algebras. Coherent states are given for different generators of the \(q\)-oscillator algebra defined by the relations \([a_ -,a_ +]_ q=q^{-N}\), \([N,a_ \pm]=\pm a_ \pm\), where \([a,b]_ q=ab-qba\), \([a,b]=ab-ba\). For these coherent states the completeness theorem is valid. Different generalizations of \(q\)- oscillator to the case of many degrees of freedom are discussed. Applications of \(q\)-oscillators to realizations of quantum algebras and superalgebras, to deformations of Lie algebras, and to construction of physical system models (such as, for example, the deformed Jaynes- Cummings model) are considered.
Reviewer: A.Klimyk (Kiev)

MSC:

17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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