Maxime Wagner | Searcharxiv

arXiv2025

Hamiltonian dynamics and geometry on the two-plectic six-sphere

We study the two-plectic geometry of the six-sphere induced by pulling back a canonical $G_2$-invariant three-form from $\mathbb{R}^7$ . Notably we explicitly prove non-flatness of this structure and show that its infinitesimal automorphisms are given by the exceptional Lie algebra $\mathfrak{g}_2$. Several interesting classes of solutions of the dynamical Hamilton-de Donder-Weyl equations with one- and two-dimensional sources are exhibited.

math.DG↗

arXiv2024

Notes on equivalent formulations of Hamiltonian dynamics on multicotangent bundles

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.

math.SG↗