# Putting an Edge to the Poisson Bracket

Source: [Putting an Edge to the Poisson Bracket](<https://www.sota2.com/research/paper/68fa24a92c2a3760193a73dc>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T09:24:26.405Z

Authors: K. Bering

Published: 1998-06-30T21:52:40.000Z

## Abstract

We consider a general formalism for treating a Hamiltonian (canonical) field theory with a spatial boundary. In this formalism essentially all functionals are differentiable from the very beginning and hence no improvement terms are needed. We introduce a new Poisson bracket which differs from the usual \`\`bulk'' Poisson bracket with a boundary term and show that the Jacobi identity is satisfied. The result is geometrized on an abstract world volume manifold. The method is suitable for studying systems with a spatial edge like the ones often considered in Chern-Simons theory and General Relativity. Finally, we discuss how the boundary terms may be related to the time ordering when quantizing.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/hep-th/9806249>)

[PDF](<https://arxiv.org/pdf/hep-th/9806249.pdf>)