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arXiv · q-alg/9503017

Geometry of Deformed Boson Algebras

P. Crehan·T. G. Ho
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Abstract

Phase-space realisations of an infinite parameter family of quantum deformations of the boson algebra in which the $q$-- and the $qp$--deformed algebras arise as special cases are studied. Quantum and classical models for the corresponding deformed oscillators are provided. The deformation parameters are identified with coefficients of non-linear terms in the normal forms expansion of a family of classical Hamiltonian systems. These quantum deformations are trivial in the sense that they correspond to non-unitary transformations of the Weyl algebra. They are non-trivial in the sense that the deformed commutators consistently quantise a class of non-canonical classical Poisson structures.

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BibTeXRIS

P. Crehan, T. G. Ho. 1995-03-30. Geometry of Deformed Boson Algebras. https://doi.org/10.1142/s0129055x96000342

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