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

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 formal energy for a parametrized version of the Hilbert--Einstein Lagrangian and we show that this quantity is conserved.

arXiv comment9 pages, slightly revised, to appear in Proc. Winter School "Geometry and Physics", Srni (CZ) 2006

References in corpus (3)

• Extended Hamiltonian systems in multisymplectic field theories
• Covariant Hamiltonian formalism for the calculus of variations with several variables
• A New Geometric Proposal for the Hamiltonian Description of Classical Field Theories