Notes on equivalent formulations of Hamiltonian dynamics on multicotangent bundles

Abstract

We show the equivalence of five different conditions on a classical field $\ddot{I}ˆ$ with values in a restricted multicotangent bundle to be a solution of the field equations, notably in terms of the Hamilton-Volterra equations, the principle of least action and several conditions based on the contraction of the multi-vector tangent to $\ddot{I}ˆ$ with canonical differential forms. Most prominently, we have equivalence to the "dynamical Hamilton-de Donder-Weyl equation", that can be vastly generalized to define Hamiltonian dynamics on multisymplectic manifolds, defined for sources of different dimensions.

We (slightly) changed the title, added mathematical details, and corrected linguistic and typographical mistakes. 19 pages