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QUANTUM DEFORMATIONS OF QUANTUM MECHANICS

Modern Physics Letters A, 1993
Based on a deformation of the quantum mechanical phase space we study q-deformations of quantum mechanics for qk=1 and 0<q<1. After defining a q-analog of the scalar product on the function space we discuss and compare the time evolution of operators in both cases.
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Euclidean quantum mechanics

Physical Review A, 1987
Euclidean quantum mechanics is not limited to an analytical continuation in time from the Schr\"odinger equation to the heat equation. It is a new classical statistical theory founded on a new probabilistic interpretation of the heat equation and constitutes the closest classical analogy of quantum mechanics.
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Precausal quantum mechanics

Physical Review A, 1987
It is pointed out that both classical Wheeler-Feynman electrodynamics and its finite quantized generalization inevitably lead to microscopic causality violation. As there is some evidence for such effects in proton Compton scattering, there is possibly reason to prefer such absorber theories of action at a distance over field theories as the more ...
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Topological quantum mechanics

Physical Review D, 1991
The quantum theory of a type of generally covariant field theory, that has no local degrees of freedom, is described. Physical observables that capture topological properties of the manifold are identified and a representation of their Poisson algebra is constructed to obtain the quantum theory.
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Discrete quantum mechanics

Journal of Mathematical Physics, 1986
A discrete model for quantum mechanics is presented. First a discrete phase space S is formed by coupling vertices and edges of a graph. The dynamics is developed by introducing paths or discrete trajectories in S. An amplitude function is used to compute probabilities of quantum events and a discrete Feynman path integral is presented.
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