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

## TL;DR

This paper presents a practical geometric method for implementing Dirac's algorithm in constrained field theories with boundaries, addressing boundary-specific issues and illustrating with relevant examples including general relativity.

## Contribution

It introduces a boundary-aware geometric approach to Dirac's algorithm for constrained fields, expanding the GNH framework to boundary-involved systems.

## Key findings

- Effective handling of boundary conditions in Dirac's algorithm
- Application to field theories related to general relativity
- Clarification of geometric structures in constrained systems with boundaries

## 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.