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arXiv · 1705.05818

Noether's Theorem in Multisymplectic Geometry

Jonathan Herman
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Abstract

We extend Noether's theorem to the setting of multisymplectic geometry by exhibiting a correspondence between conserved quantities and continuous symmetries on a multi-Hamiltonian system. We show that a homotopy co-momentum map interacts with this correspondence in a way analogous to the moment map in symplectic geometry. We apply our results to generalize the theory of the classical momentum and position functions from the phase space of a given physical system to the multisymplectic phase space. We also apply our results to manifolds with a torsion-free $G_2$ structure.

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Jonathan Herman. 2017-11-14. Noether's Theorem in Multisymplectic Geometry. https://doi.org/10.1016/j.difgeo.2017.09.003

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