Covariant Poisson Brackets for Classical Fields

摘要

Poisson brackets that are covariant under spacetime coordinate changes are presented for relativistic field theories. The formalism described here is an alternative to the sympletic formulation of field theories and has several advantages. It applies to relativistic fluids and plasmas written in Eulerian variables, while the symplectic formulation does not. It is expected to simplify and clarify the transition to the dynamical (or 3+1) Hamiltonian formalism as well. (ERA citation 10:023300)