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2020 On Gibbs States of Mechanical Systems with Symmetries
Charles-Michel Marle
J. Geom. Symmetry Phys. 57: 45-85 (2020). DOI: 10.7546/jgsp-57-2020-45-85

Abstract

The French mathematician and physicist Jean-Marie Souriau studied Gibbs states for the Hamiltonian action of a Lie group on a symplectic manifold and considered their possible applications in Physics and Cosmology. These Gibbs states are presented here with detailed proofs of all the stated results. A companion paper to appear will present examples of Gibbs states on various symplectic manifolds on which a Lie group of symmetries acts by a Hamiltonian action, including the Poincaré disk and the Poincaré half-plane.

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Charles-Michel Marle. "On Gibbs States of Mechanical Systems with Symmetries." J. Geom. Symmetry Phys. 57 45 - 85, 2020. https://doi.org/10.7546/jgsp-57-2020-45-85

Information

Published: 2020
First available in Project Euclid: 30 December 2020

MathSciNet: MR4194211
Digital Object Identifier: 10.7546/jgsp-57-2020-45-85

Rights: Copyright © 2020 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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