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Noether's Theorem in Multisymplectic Geometry. (arXiv:1705.05818v1 [math.SG])
来源于:arXiv
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. 查看全文>>