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

Abstract

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 illustrate the main features of our approach.

arXiv comment25 pages

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• Quantum Chern-Simons theories on cylinders: BV-BFV partition functions
• Canonical analysis of field theories in the presence of boundaries: Maxwell+Pontryagin
• Euclidean self-dual gravity: Ashtekar variables without gauge fixing
• On covariant and canonical Hamiltonian formalisms for gauge theories
• Weakly Isolated Horizons: $3+1$ decomposition and canonical formulations in self-dual variables
• Edge observables of the Maxwell-Chern-Simons theory
• Dynamical time and Ashtekar variables for the Husain-Kuchař model
• On covariant and canonical Hamiltonian formalisms: Weakly Isolated Horizons
• Three roads to the geometric constraint formulation of gravitational theories with boundaries
• A note on the Hamiltonian structure of transgression forms
• Consistent and non-consistent deformations of gravitational theories
• Hidden diffeos in the Hamiltonian formulation of a background independent field theory