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

TL;DR

This paper extends the Skinner--Rusk formalism to multicontact geometrical structures, enabling unified Lagrangian and Hamiltonian descriptions of action-dependent classical field theories, with applications to electromagnetism in media.

Contribution

It introduces a multicontact Skinner--Rusk formalism that unifies Lagrangian and Hamiltonian approaches for action-dependent field theories, including singular cases.

Findings

Unified formalism for action-dependent theories.

Application to electromagnetism in media.

Framework for singular theories.

Abstract

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.