Putting an edge to the Poisson bracket

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. (C) 2000 American Institute of Physics. [S0022- 2488(00)00708-8].