  It is shown that the nature of physical time requires the extended
phase-space in mechanics to have a bundle structure with time as the
1-dimensional base manifold and the phase space as the fiber. This bundle
picture of the extended phase space is then applied to fields in a covariant,
`directly' Hamiltonian formalism. Variational principle in the covariant
phase-space is discussed, Noether currents calculated for symmetry fields and a
new bracket analogous to the Peierls bracket is defined.
