Damaskinskij, E. V.; Kulish, P. P. Deformed oscillators and their applications. (Russian. English summary) Zbl 0744.17010 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 189, 37-74 (1991). 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) Cited in 1 ReviewCited in 8 Documents MSC: 17B37 Quantum groups (quantized enveloping algebras) and related deformations 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory Keywords:\(q\)-oscillators; contractions of quantum algebras; deformed Jaynes- Cummings model; coherent states PDFBibTeX XMLCite \textit{E. V. Damaskinskij} and \textit{P. P. Kulish}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 189, 37--74 (1991; Zbl 0744.17010) Full Text: EuDML