Projective representation of the Galilei group for classical and quantum-classical systems

• URL: http://arxiv.org/abs/2107.03623v2
• Date: Thu, 23 Feb 2023 18:26:23 GMT
• Title: Projective representation of the Galilei group for classical and quantum-classical systems
• Authors: A.D. Berm\'udez Manjarres
• Abstract summary: A unitary irreducible non-projective representation of the Galilei group is possible in the Koopman-von Neumann formulation of classical mechanics. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Non-relativistic tachyons: a new representation of the Galilei group [0.0]
  We arrive at a consistent, nonstandard representation of the Galilei group. The corresponding quantum (and classical) theory shares with the relativistic one their fundamentals. The tachyonic objects described by the new representation cannot be regarded as localizable in the standard sense.
  arXiv  Detail & Related papers  (2024-07-22T08:26:40Z)
• A Universal Kinematical Group for Quantum Mechanics [0.0]
  In 1968, Dashen and Sharp obtained a certain singular Lie algebra of local densities and currents from canonical commutation relations in nonrelativistic quantum field theory. The corresponding Lie group is infinite dimensional: the natural semidirect product of an additive group of scalar functions with a group of diffeomorphisms.
  arXiv  Detail & Related papers  (2024-04-28T18:46:24Z)
• Galilean Relativity and the Path Integral Formalism in Quantum Mechanics [0.0]
  In quantum mechanics Galilean boosts require a non-trivial transformation rule for the wave function. The representation of certain symmetry groups in quantum mechanics can be simply understood in terms of the transformation properties of the classical Lagrangian.
  arXiv  Detail & Related papers  (2023-06-23T13:09:19Z)
• Phase space ensembles for classical and quantum-classical systems [0.0]
  We develop a theory of ensembles in phase space and use it to investigate the construction of a quantum-classical hybrid theory. Our approach points out a possible connection between two previously unrelated hybrid systems.
  arXiv  Detail & Related papers  (2023-05-03T04:03:56Z)
• Does the Universe have its own mass? [62.997667081978825]
  The mass of the universe is a distribution of non-zero values of gravitational constraints. A formulation of the Euclidean quantum theory of gravity is also proposed to determine the initial state. Being unrelated to ordinary matter, the distribution of its own mass affects the geometry of space.
  arXiv  Detail & Related papers  (2022-12-23T22:01:32Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• Galilean covariance of quantum-classical hybrid systems of the Sudarshan type [0.0]
  We show that these kind of hybrids cannot be given as a unitary representation of the Galilei group and at the same time conserve the total linear momentum.
  arXiv  Detail & Related papers  (2020-12-03T23:13:36Z)
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain [21.24186888129542]
  We study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves.
  arXiv  Detail & Related papers  (2020-10-14T16:46:11Z)
• Classical non-equilibrium statistical mechanics and an "open system dynamics" perspective on quantum-classical analogy [4.592848943542229]
  We develop a time-local equation of motion using Green's functions and a series expansion method. We compare this equation of motion with its supposed quantum counterpart, namely the quantum master equation. We notice an apparent exception to QCA in this case, as the first-order classical equation of motion derived herein contains a term that does not appear to have a quantum analogue.
  arXiv  Detail & Related papers  (2020-05-18T13:49:13Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.