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arXiv · 2410.21068

Notes on equivalent formulations of Hamiltonian dynamics on multicotangent bundles

Maxime Wagner·Tilmann Wurzbacher
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Abstract

We show the equivalence of five different conditions on a classical field $\psi$ 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 $\psi$ 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.

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Maxime Wagner, Tilmann Wurzbacher. 2024-10-28. Notes on equivalent formulations of Hamiltonian dynamics on multicotangent bundles. https://arxiv.org/abs/2410.21068

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