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Zbl 0984.70020
Bering, K.
Putting an edge to the Poisson bracket. (English)
[J] J. Math. Phys. 41, No.11, 7468-7500 (2000). ISSN 0022-2488; ISSN 1089-7658/e

Summary: 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 in general relativity. Finally, we discuss how the boundary terms may be related to the time ordering when quantizing.

MSC 2000:: *70S05 Lagrangian formalism and Hamiltonian formalism
70G45 Differential-geometric methods

Keywords: Hamiltonian canonical field theory; Poisson bracket; boundary term; Jacobi identity; abstract world volume manifold; spatial edge; Chern-Simons theory; general relativity; time ordering

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