Covariant Poisson Brackets for Classical Fields
Marsden, J. E., R. Montgomery, P. J. Morrison, and W. B. Thompson
Annals of Physics, 169 (1986), 29-47
Abstract:
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.