Constructing Poisson algebras

(Commutative) Poisson algebras are clearly very interesting, so it would be nice to have ways of constructing examples. We know that is a Poisson algebra with bracket uniquely defined by ; this describes a classical particle in one dimension, and is the classical limit of a quantum particle in one dimension (essentially the Weyl algebra). [...]

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Poisson algebras and the classical limit

In the previous post we described the Heisenberg picture of quantum mechanics, which can be phrased quite generally as follows: given a noncommutative algebra (the algebra of observables of some quantum system) and a Hamiltonian , we obtain a derivation , which is (up to some scalar multiple) the infinitesimal generator of time evolution. This [...]

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