The Geometry of the solution space of first order Hamiltonian field theories III: Palatini's formulation of General Relativity

2023/11/27 by Ciaglia, Florio M., Di Cosmo, Fabio, Ibort, Alberto +3
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2311.15714

Abstract

We complete the program started in two companion papers of defining a Poisson bracket structure on the space of solutions of the equations of motion of first order Hamiltonian field theories. The case of General Relativity is addressed by looking at it as a particular non-Abelian gauge theory in a suitable low-energy limit and via a technique related to the coisotropic embedding theorem.

Related

• The Geometry of the solution space of first order Hamiltonian field theories II: non-Abelian gauge theories
• Reduction to first order of the Hamiltonian Constraint of General Relativity
• From Lagrangian to Hamiltonian formulations of the Palatini action
• Palatini Approach Beyond Einstein's Gravity
• Reduction of the canonical Hamiltonian of the metric GR to its natural form