Putting an Edge to the Poisson Bracket

Details Putting an Edge to the Poisson Bracket Putting an Edge to the Poisson Bracket

1998-06-30

arxiv.org/abs/hep-th/9806249v3

J.Math.Phys. 41 (2000) 7468-7500

Physics

High Energy Physics

High Energy Physics - Theory

36 pages, LaTeX. v2: A manifest formulation of the Poisson bracket and some examples are added, corrected a claim in Appendix

Scientific paper

10.1063/1.1286144

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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