Geometry of multisymplectic Hamiltonian first-order field theories (Q2738259)

The authors survey covariant Hamiltonian formalism for first-order field theories within the context of multisymplectic manifolds. It is well-known that, in the multisymplectic description of field theories, there are several choices for the multimomentum bundle where the covariant Hamiltonian formalism takes place. As a consequence, several proposals for this formalism can be stated. In this work, an accuracy study of some of these Hamiltonian formalisms is done, showing their equivalence. In particular, the geometrical structures needed for the Hamiltonian formalism are introduced and compared, and the derivation of Hamiltonian field equations from the corresponding variational principle is shown in detail. The authors also perform a study of Hamiltonian systems associated with both hyper-regular and almost regular Lagrangian systems. The role of connections in the construction of Hamiltonian field theories is clarified. Two examples are given finally: nonautonomous mechanics, and the electromagnetic field (with fixed background). This is an exhaustive and well-written paper which illustrates the role of different geometric structures involved in covariant Hamiltonian field theories, and gives an accurate and clarifying survey of many results that can be found in the literature.