Projective representation of the Galilei group for classical and quantum-classical systems
arXiv:2107.03623 · doi:10.1088/1751-8121/ac28cc
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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Cited by in corpus (6)
- Evolution of hybrid quantum-classical wavefunctions
- Hybrid quantum-classical dynamics of pure-dephasing systems
- Operational classical mechanics: Holonomic Systems
- Lévy-Leblond Equation and Eisenhart-Duval lift in Koopman-von Neumann Mechanics
- Measurement of a quantum system with a classical apparatus using ensembles on configuration space
- Separability and entanglement in classical eigenfunctions as a criterion for Hamiltonian chaos