Publication details
Putting an Edge to the Poisson Bracket
| Authors | |
|---|---|
| Year of publication | 2000 |
| Type | Article in Periodical |
| Magazine / Source | JOURNAL OF MATHEMATICAL PHYSICS |
| MU Faculty or unit | |
| Citation | |
| web | http://arxiv.org/abs/hep-th/9806249 |
| Doi | https://doi.org/10.1063/1.1286144 |
| Field | Theoretical physics |
| Keywords | FIELD-THEORY; VARIABLES |
| Description | 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. |