Some aspects of the homogeneous formalism in Field Theory and gauge invariance

摘要

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