Proof of the equivalence of the symplectic forms derived from the canonical and the covariant phase space formalisms

Abstract

We prove that, for any theory defined over a space-time with boundary, the symplectic form derived in the covariant phase space is equivalent to the one derived from the canonical formalism.

Accepted in PRD

References in corpus (12)

• Black Holes in Higher-Derivative Gravity
• Edge modes of gravity -- I: Corner potentials and charges
• Extended corner symmetry, charge bracket and Einstein's equations
• Geometric formulation of the Covariant Phase Space methods with boundaries
• Null infinity as an open Hamiltonian system
• Brown-York charges with mixed boundary conditions
• Covariant phase space for gravity with boundaries: metric vs tetrad formulations
• Gravitational $SL(2,\mathbb{R})$ Algebra on the Light Cone
• Concise symplectic formulation for tetrad gravity
• Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action
• Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables
• On the on-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries

Cited by in corpus (8)

• Finite Charges from the Bulk Action
• On the covariant formulation of gauge theories with boundaries
• Canonical aspects of pregeometric vector-based first order gauge theory
• On covariant and canonical Hamiltonian formalisms for gauge theories
• On covariant and canonical Hamiltonian formalisms: Weakly Isolated Horizons
• Spontaneous particle creation by oscillating compact stars
• Phase space for gravity with boundaries
• Multisymplectic Formalism for Cubic Horndeski Theories