Hyperbolic Quantum Mechanics as Deformation of Conventional Classical Mechanics
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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