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

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.