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Wigner Quantization and Lie Superalgebra Representations

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Lie Theory and Its Applications in Physics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 36))

Abstract

T.D. Palev laid the foundations of the investigation of Wigner quantum systems through representation theory of Lie superalgebras. His work has been very influential, in particular on my own research. It is quite remarkable that the study of Wigner quantum systems has had some impact on the development of Lie superalgebra representations. In this review paper, I will present the method of Wigner quantization and give a short overview of systems (Hamiltonians) that have recently been treated in the context of Wigner quantization. Most attention will go to a system for which the quantization conditions naturally lead to representations of the Lie superalgebra \(\mathfrak{o}\mathfrak{s}\mathfrak{p}(1\vert 2n)\). I shall also present some recent work in collaboration with G. Regniers, where generating functions techniques have been used in order to describe the energy and angular momentum contents of 3-dimensional Wigner quantum oscillators.

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Acknowledgements

This research was supported by project P6/02 of the Interuniversity Attraction Poles Programme (Belgian State—Belgian Science Policy).

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, 9000, Gent, Belgium

    Joris Van der Jeugt

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  1. Joris Van der Jeugt
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Correspondence to Joris Van der Jeugt .

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Editors and Affiliations

  1. Bulgarian Academy of Sciences, 72 Tsarigradsko Chaussee, Sofia, 1784, Sofiya, Bulgaria

    Vladimir Dobrev

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Van der Jeugt, J. (2013). Wigner Quantization and Lie Superalgebra Representations. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 36. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54270-4_10

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