Covariant momentum map thermodynamics for parametrized field theories

2019/11/30 by Goffredo Chirco, Marco Laudato, Fabio M. Mele · 8 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Cosmology and Gravitation Theories #Covariant transformation #Gauge anomaly #Gauge covariant derivative #Gauge symmetry #Gauge theory #Introduction to gauge theory #Mathematical physics #Physics #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Spacetime symmetries #Statistical Mechanics and Entropy #Theoretical physics #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1142/s0219887821500183

published in International Journal of Geometric Methods in Modern Physics 18(02), 2150018 (World Scientific) · 46 pages, 1 figure

arxiv created 2020/08/17 · arxiv updated 2020/11/12 · openalex publication_date 2020/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Momentum Maps and Classical Relativistic Fields. Part II: Canonical Analysis of Field Theories
• Quantization of Gauge Systems
• On the multisymplectic formalism for first order field theories
• STRING THEORY, QUANTUM MECHANICS AND NONCOMMUTATIVE GEOMETRY: A NEW PERSPECTIVE ON THE GRAVITATIONAL DYNAMICS OF D0-BRANES
• The theory of gravitation in Hamiltonian form
• Information Theory and Statistical Mechanics
• Covariant phase space formulation of parametrized field theories
• Time in quantum gravity: An hypothesis
• Gauge transformations in the Lagrangian and Hamiltonian formalisms of generally covariant theories
• Universality of Gravity from Entanglement
• Republication of: The dynamics of general relativity
• Emergent spacetime and the origin of gravity
• Prima facie questions in quantum gravity
• Space-time covariant form of Ashtekar’s constraints
• Information Geometry and Its Applications
• Statistical discrete geometry
• Group field theory as the 2nd quantization of Loop Quantum Gravity
• Souriau Exponential Map Algorithm for Machine Learning on Matrix Lie Groups
• Partial observables
• On A Covariant Hamiltonian Description of Palatini's Gravity on Manifolds with Boundary
• Momentum Maps and Classical Relativistic Fields. Part I: Covariant Field Theory