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Putting an edge to the Poisson bracket. (English) Zbl 0984.70020
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:
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
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