Hyperbolic Quantum Mechanics as Deformation of Conventional Classical Mechanics

  • Andrei Khrennikov
Part of the Fundamental Theories of Physics book series (FTPH, volume 160)


We develop Fourier analysis over the hyperbolic algebra. We demonstrate that classical mechanics has, besides the well-known quantum deformation over complex numbers, another deformation, namely, hyperbolic quantum mechanics. The classical Poisson bracket can be obtained as the limit h→0 not only of the ordinary Moyal bracket, but also a hyperbolic analogue of the Moyal bracket.


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Copyright information

© Springer Science + Business Media B.V. 2009

Authors and Affiliations

  1. 1.International Center for Mathematical Modeling in Physics and Cognitive ScienceUniversity of VäxjöVäxjöSweden

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