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.

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Cited by in corpus (5)

• Projective representation of the Galilei group for classical and quantum-classical systems
• Galilean covariance of quantum-classical hybrid systems of the Sudarshan type
• The Schwinger action principle for classical systems
• Operational classical mechanics: Holonomic Systems
• Unitary representation of the Poincaré group for classical relativistic dynamics