# Dirac’s algorithm in the presence of boundaries: a practical guide to a geometric approach

@article{JFernandoBarbero2019DiracsAI, title={Dirac’s algorithm in the presence of boundaries: a practical guide to a geometric approach}, author={G. J.FernandoBarbero and Bogar D'iaz and Juan Margalef-Bentabol and Eduardo J S Villase{\~n}or}, journal={Classical and Quantum Gravity}, year={2019} }

The goal of this paper is to propose and discuss a practical way to implement the Dirac algorithm for constrained field models defined on spatial regions with boundaries. Our method is inspired in the geometric viewpoint developed by Gotay, Nester, and Hinds (GNH) to deal with singular Hamiltonian systems. We pay special attention to the specific issues raised by the presence of boundaries and provide a number of significant examples -among them field theories related to general relativity- to… Expand

#### 12 Citations

Three Roads to the Geometric Constraint Formulation of Gravitational Theories with Boundaries

- Computer Science, Physics
- Symmetry
- 2021

Other approaches to the Hamiltonian description of mechanical or field models defined by singular Lagrangians that rely on the direct use of the equations of motion (and the tangency requirements characteristic of the Gotay, Nester and Hinds method), or are formulated in the tangent bundle of the configuration space are discussed. Expand

Generalizations of the Pontryagin and Husain-Kuchař actions to manifolds with boundary

- Physics, Mathematics
- Journal of High Energy Physics
- 2019

Abstract
In this paper we study a family of generalizations of the Pontryagin and Husain-Kuchǎr actions on manifolds with boundary. In some cases, they describe well- known models — either at the… Expand

Constructing the theory at the boundary, its dynamics and degrees of freedom

- Physics, Mathematics
- 2020

Given a theory in a region of space-time with boundaries, defined by a Lagrangian, we propose a method to find the corresponding theory at the boundary (either space-like or time-like), that allows… Expand

Constrained systems, generalized Hamilton-Jacobi actions, and quantization

- Physics, Mathematics
- 2020

Mechanical systems (i.e., one-dimensional field theories) with constraints are the focus of this paper. In the classical theory, systems with infinite-dimensional targets are considered as well (this… Expand

Hamiltonian GNH analysis of the parametrized unimodular extension of the Holst action

- Physics, Mathematics
- 2021

We give a detailed account of the Hamiltonian GNH analysis of the parametrized unimodular extension of the Holst action. The purpose of the paper is to derive, through the clear geometric picture… Expand

Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action

- Physics
- 2021

We give a detailed account of the Hamiltonian Gotay-Nester-Hinds (GNH) analysis of the parametrized unimodular extension of the Holst action. The purpose of the paper is to derive, through the clear… Expand

Quantum field theory with dynamical boundary conditions and the Casimir effect

- Physics, Mathematics
- 2020

We study a coupled system that describes the interacting dynamics between a bulk field, confined to a finite region with timelike boundary, and a boundary observable. In our system the dynamics of… Expand

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- Mathematics, Computer Science
- Symmetry
- 2019

It is shown how the electric-magnetic duality symmetry of the electromagnetic field and the Aharonov–Bohm effect can be derived from the simple harmonic oscillator character of vacuum electrodynamics, while also demonstrating how the magnetic version of the latter naturally arises in an explicitly non-local manner. Expand

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- Physics, Mathematics
- 2020

We compute partition functions of Chern–Simons type theories for cylindrical spacetimes I×Σ, with I an interval and dim Σ = 4l+2, in the BVBFV formalism (a refinement of the Batalin–Vilkovisky… Expand

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- Physics, Mathematics
- 2021

We discuss a simple symplectic formulation for tetrad gravity that leads to the real Ashtekar variables in a direct and transparent way. It also sheds light on the role of the Immirzi parameter and… Expand

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