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- W2138751661 abstract "We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently." @default.
- W2138751661 created "2016-06-24" @default.
- W2138751661 creator A5049413367 @default.
- W2138751661 date "2013-07-01" @default.
- W2138751661 modified "2023-10-18" @default.
- W2138751661 title "Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras" @default.
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- W2138751661 doi "https://doi.org/10.1063/1.4816086" @default.
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