  We propose a suitable formulation of the Hamiltonian formalism for Field
Theory in terms of Hamiltonian connections and multisymplectic forms where a
composite fibered bundle, involving a line bundle, plays the role of an
extended configuration bundle. This new approach can be interpreted as a
suitable generalization to Field Theory of the homogeneous formalism for
Hamiltonian Mechanics. As an example of application, we obtain the expression
of a formal energy for a parametrized version of the Hilbert--Einstein
Lagrangian and we show that this quantity is conserved.
