Abstract
It is possible to give a complete description of Classical Mechanics in terms of symplectic geometry and Poisson bracket. It is the essential of the hamiltonian formalism. In a common programm with M. Flato, C. Fronsdal and the late J. Vey, we have studied properties and applications of the deformations of a trivial associative algebra and of the Poisson Lie algebra of a symplectic manifold. Such deformations give a new invariant approach for Quantum Mechanics. I consider here only dynamical systems with a finite number of degrees of freedom, but the approach and a significative part of the results can be extended to physical fields.
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© 1988 Kluwer Academic Publishers
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Lichnerowicz, A. (1988). Applications of the Deformations of the Algebraic Structures to Geometry and Mathemetical Physics. In: Hazewinkel, M., Gerstenhaber, M. (eds) Deformation Theory of Algebras and Structures and Applications. NATO ASI Series, vol 247. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3057-5_17
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DOI: https://doi.org/10.1007/978-94-009-3057-5_17
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