Classical dynamics from a unitary representation of the Galilei group

Abstract

We give a formulation of classical mechanics in the language of operators acting on a Hilbert space. The formulation given comes from a unitary irreducible representation of the Galilei group that is compatible with the basic postulates of classical mechanics, particularly the absence of an uncertainty principle between the position and momentum of a particle. It is shown that the theory exposed in the article contains the Koopman-von Neumann formalism of classical mechanics as a particular case.

References in corpus (2)

• Perturbation theory via Feynman diagrams in classical mechanics
• Quantum-classical interactions and measurement: a consistent description using statistical ensembles on configuration space

Cited by in corpus (2)

• Galilean covariance of quantum-classical hybrid systems of the Sudarshan type
• Unitary representation of the Poincaré group for classical relativistic dynamics