# Geometric formulation of the covariant phase space methods with boundaries

@article{MargalefBentabol2021GeometricFO, title={Geometric formulation of the covariant phase space methods with boundaries}, author={Juan Margalef-Bentabol and Eduardo J S Villase{\~n}or}, journal={Physical Review D}, year={2021}, volume={103}, pages={025011} }

We analyze in full detail the geometric structure of the covariant phase space (CPS) of any local field theory defined over a space-time with boundary. To this end, we introduce a new frame: the ``relative bicomplex framework.'' It is the result of merging an extended version of the ``relative framework'' (initially developed in the context of algebraic topology by R. Bott and L. W. Tu in the 1980s to deal with boundaries) and the variational bicomplex framework (the differential geometric…

## 15 Citations

On-shell equivalence of general relativity and Holst theories with nonmetricity, torsion, and boundaries

- MathematicsPhysical Review D
- 2022

: We study a generalization of the Holst action where we admit nonmetricity and torsion in manifolds with timelike boundaries (both in the metric and tetrad formalism). We prove that its space of…

Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables

- MathematicsPhysical Review D
- 2021

We prove the equivalence in the covariant phase space of the metric and connection formulations for Palatini gravity, with nonmetricity and torsion, on a spacetime manifold with boundary. To this…

Edge modes as dynamical frames: charges from post-selection in generally covariant theories

- Physics
- 2022

We develop a framework based on the covariant phase space formalism that identiﬁes gravitational edge modes as dynamical reference frames. Previously considered in gauge theory [1], this construction…

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

- MathematicsPhysical Review D
- 2022

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.

Symmetries and Covariant Poisson Brackets on Presymplectic Manifolds

- Mathematics, PhysicsSymmetry
- 2022

As the space of solutions of the first-order Hamiltonian field theory has a presymplectic structure, we describe a class of conserved charges associated with the momentum map, determined by a…

Barnich–Troessaert bracket as a Dirac bracket on the covariant phase space

- PhysicsClassical and Quantum Gravity
- 2021

The Barnich–Troessaert bracket is a proposal for a modified Poisson bracket on the covariant phase space for general relativity. The new bracket allows us to compute charges, which are otherwise not…

Brown-York charges with mixed boundary conditions

- MathematicsJournal of High Energy Physics
- 2021

Abstract
We compute the Hamiltonian surface charges of gravity for a family of conservative boundary conditions, that include Dirichlet, Neumann, and York’s mixed boundary conditions defined by…

Chiral massive news: null boundary symmetries in topologically massive gravity

- Physics
- 2021

We study surface charges on a generic null boundary in three dimensional topological massive gravity (TMG). We construct the solution phase space which involves four independent functions over the…

Covariant phase space for gravity with boundaries: Metric versus tetrad formulations

- MathematicsPhysical Review D
- 2021

We use covariant phase space methods to study the metric and tetrad formulations of General Relativity in a manifold with boundary and compare the results obtained in both approaches. Proving their…

Covariant phase space with null boundaries

- PhysicsCommunications in Theoretical Physics
- 2021

By imposing the boundary condition associated with the boundary structure of the null boundaries rather than the usual one, we find for Einstein's gravity that the variational principle works only in…

## References

SHOWING 1-10 OF 69 REFERENCES

Covariant phase space with boundaries

- Physics
- 2019

The covariant phase space method of Iyer, Lee, Wald, and Zoupas gives an elegant way to understand the Hamiltonian dynamics of Lagrangian field theories without breaking covariance. The original…

Covariant phase space, constraints, gauge and the Peierls formula

- Physics
- 2014

It is well known that both the symplectic structure and the Poisson brackets of classical field theory can be constructed directly from the Lagrangian in a covariant way, without passing through the…

On Covariant Phase Space and the Variational Bicomplex

- Mathematics
- 2004

The notion of a phase space in classical mechanics is well known. The extension of this concept to field theory however, is a challenging endeavor, and over the years numerous proposals for such a…

Momentum maps and classical relativistic fields. Part 1: Covariant Field Theory

- Physics
- 1997

This is the first paper of a five part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections…

Natural Boundary Conditions in Geometric Calculus of Variations

- Mathematics
- 2013

Abstract In this paper we obtain natural boundary conditions for a large class of variational problems with free boundary values. In comparison with the already existing examples, our framework…

Isolated horizons: The Classical phase space

- Physics
- 1999

A Hamiltonian framework is introduced to encompass non-rotating (but possibly charged) black holes that are “isolated” near future time-like infinity or for a finite time interval. The underlying…

Hamiltonian treatment of linear field theories in the presence of boundaries: a geometric approach

- Physics
- 2013

The purpose of this paper is to study in detail the constraint structure of the Hamiltonian and symplectic-Lagrangian descriptions for the scalar and electromagnetic fields in the presence of spatial…

Local symmetries and constraints

- Mathematics
- 1990

The general relationship between local symmetries occurring in a Lagrangian formulation of a field theory and the corresponding constraints present in a phase space formulation are studied. First, a…