Quantum theory phase space foundations

Abstract

We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain probability, hence resembling the classical statistical theory in which coordinates and momenta are well measurable quantities. The search is for the classical object best describing the quantum state, while the physical observables of the quantum theories are operators.