Abstract
A Poisson bracket structure is defined on associative algebras which allows for a generalized Hamiltonian dynamics. Both classical and quantum mechanics are shown to be special cases of the general formalism.
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References
P. A. M. Dirac,The Principles of Quantum Mechanics (Oxford University Press, Oxford, 1958), p. 113.
R. Abraham and J.E. Marsden,Foundations of Mechanics (Benjamin/Cummings, Reading, Massachusetts, 1978).
G. C. Sherry,Found. Phys. 19, 773 (1989).
P. J. Olver,Applications of Lie Groups to Differential Equations (Springer, New York, 1986).
P. Libermann and C.-M. Marle,Symplectic Geometry and Analytical Mechanics (Reidel, Dordrect, 1987).
A. Heslot,Phys. Rev. 31D, 1341 (1985).
R. Hermann,Quantum and Fermion Differential Geometry, Part A (Math. Sci. Press, Brookline, 1977).
A. Crumeyrolle, inClifford Algebras and their Applications in Mathematical Physics, J.S.R. Chisholm, ed. (Reidel, Dordrecht, 1986), p. 517.
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Sherry, G.C. A generalized Hamiltonian formalism unifying classical and quantum mechanics. Found Phys Lett 3, 255–265 (1990). https://doi.org/10.1007/BF00666016
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DOI: https://doi.org/10.1007/BF00666016