Phase space for gravity with boundaries

Abstract

This explanatory note, based on the geometrical method by Kijovski and Tulczyjew, describes the construction of the reduced phase space of Lagrangian field theories, i.e., the correct space of initial conditions with its symplectic structure. Several examples and, in particular, the case of four-dimensional gravity in the coframe formalism (Palatini--Cartan theory) are analyzed.

23 pages. References updated. Article commissioned by the Encyclopedia of Mathematical Physics

References in corpus (7)

• Extended corner symmetry, charge bracket and Einstein's equations
• Geometric formulation of the Covariant Phase Space methods with boundaries
• First order gravity on the light front
• Proof of the equivalence of the symplectic forms derived from the canonical and the covariant phase space formalisms
• On the Mathematics of Coframe Formalism and Einstein-Cartan Theory -- A Brief Review
• Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables
• Gravitational Constraints on a Lightlike boundary