Covariant Poisson Brackets for Classical Fields

Poisson brackets that are spacetime covariant are presented for a variety of relativistic field theories. These theories include electromagnetism, general relativity, and general relativistic fluids and plasmas in Eulerian representation. The examples presented suggest the development of a general theory; the beginnings of such a theory are presented. Our covariant bracket formalism provides a general setting for, amongst other things, clarifying the transition from the covariant formalism to the dynamical 3 + 1 Hamiltonian formalism of Dirac and Arnowitt, Deser, and Misner. We illustrate the relevant procedures with electromagnetism