Chirco, Goffredo and Laudato, Marco and Mele, Fabio Maria (2021) Covariant momentum map thermodynamics for parametrized field theories. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 18 (2): 2150018. ISSN 0219-8878, 1793-6977
Full text not available from this repository. (Request a copy)Abstract
A general-covariant statistical framework capable of describing classical fluctuations of the gravitational field is a thorny open problem in theoretical physics, yet ultimately necessary to understand the nature of the gravitational interaction, and a key to quantum gravity. Inspired by Souriau's symplectic generalization of the Maxwell-Boltzmann-Gibbs equilibrium in Lie group thermodynamics, we investigate a space-time-covariant formulation of statistical mechanics for parametrized first-order field theories, as a simplified model sharing essential general covariant features with canonical general relativity. Starting from a covariant multi-symplectic phase space formulation, we define a general-covariant notion of Gibbs state in terms of the covariant momentum map associated with the lifted action of the diffeomorphisms group on the extended phase space. We show how such a covariant notion of equilibrium encodes the whole information about symmetry, gauge and dynamics carried by the theory, associated with a canonical spacetime foliation, where the covariant choice of a reference frame reflects in a Lie algebra-valued notion of local temperature. We investigate how physical equilibrium, hence time evolution, emerges from such a state and the role of the gauge symmetry in the thermodynamic description.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HAMILTONIAN-FORMALISM; STATISTICAL-MECHANICS; GAUGE; TIME; GRAVITATION; CALCULUS; DYNAMICS; GEOMETRY; General covariant Gibbs state; covariant field theories; symplectic and multi-symplectic geometry |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 16 Sep 2022 06:18 |
| Last Modified: | 16 Sep 2022 06:18 |
| URI: | https://pred.uni-regensburg.de/id/eprint/47482 |
Actions (login required)
 |
View Item |
