This review paper is devoted to presenting the standard multisymplectic formulation for
describing geometrically classical field theories, both the regular and singular cases. First …

Canonical structure of classical field theory in n dimensions is studied within the covariant
polymomentum Hamiltonian formulation of De Donder-Weyl (DW). The bi-vertical (n+ 1) …

The multisymplectic description of Classical Field Theories is revisited, including its relation
with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to …

The (pre) multisymplectic geometry of the De Donder–Weyl formalism for field theories is
further developed for a variety of field theories including a scalar field theory from the …

A new geometric structure inspired by multisymplectic and contact geometries, which we call
multicontact structure, is developed to describe non-conservative classical field theories …

In the jet bundle description of field theories (multisymplectic models, in particular), there are
several choices for the multimomentum bundle where the covariant Hamiltonian formalism …

This work provides a general overview for the treatment of symmetries in classical field
theories and (pre) multisymplectic geometry. The geometric characteristics of the relation …

A nonpertubative approach to quantum gravity using precanonical field quantization
originating from the covariant De Donder–Weyl Hamiltonian formulation, which treats space …

We state the intrinsic form of the Hamiltonian equations of first-order classical field theories
in three equivalent geometrical ways: using multivector fields, jet fields and connections …

The aim of this paper is to propose an unambiguous intrinsic formalism for higher order field
theories which avoids the arbitrariness in the generalization of the conventional description …