Lorentz-Covariant Hamiltonian formalism

The dynamics of a classical system can be expressed by means of Poisson bra ckets. In this paper we generalize the relation between the usual noncovari ant 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 c urved space is also considered with the introduction of Christoffel symbols , covariant derivatives, and curvature tensors.