Address.
Department of Mathematics, University of Torino, via C. Alberto 10, 10123 Torino, Italy
E-mail.
marcella.palese@unito.it
ekkehart@dm.unito.it
Abstract.
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 {\em formal energy} for a parametrized version of the Hilbert--Einstein Lagrangian and we show that this quantity is conserved.
AMSclassification. 53C05, 58A20, 70H05, 70S05, 83C40.
Keywords. Jets, connections, homogeneous formalism, Hamilton equations, energy, gravity.