Geometry of Deformed Boson Algebras

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.

20 pages, latex

References in corpus (5)

• Physical nonlinear aspects of classical and quantum q-oscillators
• Representations at a Root of Unity of q-Oscillators and Quantum Kac-Moody algebras
• Quantum double of Heisenberg-Weyl algebra, its universal R-matrix and their representations
• Quantum Groups,Deformed Oscillators and their Interrelations
• When are vector fields Hamiltonian?