Time boundary terms and Dirac constraints

TL;DR

This paper systematically incorporates time boundary terms into the Hamiltonian action framework using Dirac's canonical analysis, providing a unified approach applicable to various constrained systems.

Contribution

It develops a general procedure for handling time boundary terms within Dirac's method and demonstrates its application across different constrained models.

Findings

Unified treatment of boundary terms in Hamiltonian systems.

Application to diverse constrained systems.

Clarification of boundary term implications in Dirac analysis.

Abstract

Time boundary terms usually added to action principles are systematically handled in the framework of Dirac's canonical analysis. The procedure begins with the introduction of the boundary term into the integral Hamiltonian action and then the resulting action is interpreted as a Lagrangian one to which Dirac's method is applied. Once the general theory is developed, the current procedure is implemented and illustrated in various examples which are originally endowed with different types of constraints.