Lorentz-Covariant Hamiltonian formalism

The dynamics of a classical system can be expressed by means of Poisson brackets. In this paper we generalize the relation between the usual noncovariant Hamiltonian and the Poisson brackets to a covariant Hamiltonian and new brackets in the frame of Minkowski space. These brackets can be related to those used by Feynman in his derivation Maxwell's equations. The case of curved space is also considered with the introduction of Christoffel symbols, covariant derivatives, and curvature tensors.