Noether's Theorem in Multisymplectic Geometry

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.

arXiv comment36 pages. For version 2: Incorporated the referee's suggestions and fixed some typos. To appear in Differential Geometry and its Applications

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Cited by in corpus (5)

• Multisymplectic unified formalism for Einstein-Hilbert Gravity
• Reduction of multisymplectic manifolds
• Existence and Uniqueness of Weak Homotopy Moment Maps
• Homotopy momentum sections on multisymplectic manifolds
• Quantization of Polysymplectic Manifolds