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arXiv:2004.08661 · Annals of Physics

Classical dynamics from a unitary representation of the Galilei group

A.D. Bermúdez Manjarres, Marek Nowakowski, D. Batic

Published Mar 28, 2020• 6 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2020.168157

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Abstract A physically relevant unitary irreducible non-projective representation of the Galilei group is possible in the Koopman–von Neumann formulation of classical mechanics. This classical representation is characterized by the vanishing of the central charge of the Galilei algebra. This is in contrast to the quantum case where the mass plays the role of the central charge. Here we show, by direct construction, that classical mechanics also allows for a projective representation of the Galilei group where the mass is the central charge of the algebra. We extend the result to certain kind of quantum–classical hybrid systems.

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Abstract A physically relevant unitary irreducible non-projective representation of the Galilei group is possible in the Koopman–von Neumann formulation of classical mechanics. This classical representation is characterized by the vanishing of the central charge of the Galilei algebra. This is in contrast to the quantum case where the mass plays the role of the central charge. Here we show, by direct construction, that classical mechanics also allows for a projective representation of the Galilei group where the mass is the central charge of the algebra. We extend the result to certain kind of quantum–classical hybrid systems.