On Gibbs states of mechanical systems with symmetries

Autor:	Marle, Charles-Michel
Rok vydání:	2020
Předmět:	Mathematics - Differential Geometry 53D05 53D20 53D17 82B03 82B30
Druh dokumentu:	Working Paper
Popis:	Gibbs states for the Hamiltonian action of a Lie group on a symplectic manifold were studied, and their possible applications in Physics and Cosmology were considered, by the French mathematician and physicist Jean-Marie Souriau. They are presented here with detailed proofs of all the stated results. Using an adaptation of the cross product for pseudo-Euclidean three-dimensional vector spaces, we present several examples of such Gibbs states, together with the associated thermodynamic functions, for various two-dimensional symplectic manifolds, including the pseudo-spheres, the Poincar\'e disk and the Poincar\'e half-plane. Comment: 59 pages, preprint. This version differs from the previoos one by corrections of several typographical errors and addition of the expressions of the Liouville measure for the Poincar\'e disk and the Poincar\'e half-plane
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.00582 Zobrazit plný text záznamu View this record from Arxiv