Speakers: Ounéïs Gloton (IMB)

Classical mechanics can be formulated in the setting of symplectic geometry, in which the algebra of observables of a physical system is the algebra of smooth functions on a symplectic manifold. In particular, the product of observables is a commutative operation. An additional structure called the Poisson bracket makes it a Poisson <a href="http://algebra.
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In quantum mechanics, however, this commutativity is lost, but the anticommutator gives a Poisson algebra structure, which is related to Poisson algebra of the classical system in a certain way through « canonical quantization ».
The approach of deformation quantization is to see the quantum algebra as a deformation of the classical algebra in the parameter of the Planck constant, thus staying in the setting of symplectic geometry to treat quantum <a href="http://systems.

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https://indico.math.cnrs.fr/event/15542/