Harmonic Oscillator Lie Bialgebras and their Quantization
نویسندگان
چکیده
All possible Lie bialgebra structures on the harmonic oscillator algebra are explicitly derived and it is shown that all of them are of the coboundary type. A non-standard quantum oscillator is introduced as a quantization of a triangular Lie bialgebra, and a universal R-matrix linked to this new quantum algebra is presented.
منابع مشابه
Lie bialgebra quantizations of the oscillator algebra and their universal R – matrices
All coboundary Lie bialgebras and their corresponding Poisson–Lie structures are constructed for the oscillator algebra generated by {N,A+, A−,M}. Quantum oscillator algebras are derived from these bialgebras by using the Lyakhovsky and Mudrov formalism and, for some cases, quantizations at both algebra and group levels are obtained, including their universal R–matrices.
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تاریخ انتشار 1997