Skinner--Rusk formalism of action-dependent multicontact field theories

The newly developed multicontact structure, based on contact and multisymplectic geometries, provides a very general geometrical framework suitable for the treatment of action-dependent classical field theories. Having successfully applied it to formulate the Lagrangian and Hamiltonian descriptions of these theories, in the present work, the well-known Skinner–Rusk formalism is presented in this multicontact setting, which allows us to provide a combined version of both Lagrangian and Hamiltonian formalisms particularly suitable for the study and description of singular theories. As an application of this last situation, we study a modification of Maxwell’s Lagrangian of classical electromagnetism, which incorporates action-dependent terms and allows us to describe electromagnetism in material media.