14 - Automorphisms of Formal Algebras Associated by Deformation with a Symplectic Manifold

Abstract

It is possible to give a complete description of Classical Mechanics in terms of sympletic geometry and Poisson brackets. It is the essence of the Hamiltonian formalism. Deformations of the Poisson Lie algebra and deformations of the associative algebra defined by the usual product of scalar functions determine interesting formal algebras and give a new approach for quantum mechanics [2].