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After a short review of results which we recently obtained on deformations of Lie algebras associated with symplectic manifolds, we discuss physical applications and treat some examples with deformed Poisson brackets. We make explicit a connection between classical and quantum mechanics, and the theory of Dirac brackets for second class constraints, from the viewpoint of deformation theory. Finally we discuss the general Dirac constraints formalism.
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Flato et al. (1976) studied this question.
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