Boundary terms and their Hamiltonian dynamics

TL;DR

This paper discusses how to modify the Hamiltonian formalism's Poisson brackets to include divergence integrals, with examples from Einstein gravity and Yang-Mills theory, highlighting the importance of boundary terms.

Contribution

It introduces a modified Poisson bracket framework that accounts for boundary terms in Hamiltonian dynamics, demonstrated through gravity and gauge field examples.

Findings

Modified brackets incorporate boundary contributions.

Boundary terms are essential for consistent Hamiltonian formulations.

Applications shown in Einstein gravity and Yang-Mills theory.

Abstract

It is described how the standard Poisson bracket formulas should be modified in order to incorporate integrals of divergences into the Hamiltonian formalism and why this is necessary. Examples from Einstein gravity and Yang-Mills gauge field theory are given.