A survey on geometric frameworks for action-dependent classical field theories and their relationship

This work presents a comprehensive overview of three recently developed geometric frameworks for the study of classical action-dependent field theories. Specifically, we introduce the three underlying geometric structures, namely [Formula: see text]-contact, [Formula: see text]-cocontact and multicontact, and we use them to develop the Lagrangian and Hamiltonian formalisms for such theories. Finally, we analyze the relationships among these three structures in the case of trivial bundles, and we compare them with alternative definitions of multicontact structures found in the literature.