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arXiv · hep-th/9806249

Putting an Edge to the Poisson Bracket

K. Bering
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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.

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K. Bering. 1999-12-03. Putting an Edge to the Poisson Bracket. https://doi.org/10.1063/1.1286144

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