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Noether's Theorem in Multisymplectic Geometry
- Source :
- Differential Geometry and its Applications, 2017
- Publication Year :
- 2017
-
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.<br />Comment: 36 pages. For version 2: Incorporated the referee's suggestions and fixed some typos. To appear in Differential Geometry and its Applications
- Subjects :
- Mathematics - Symplectic Geometry
Mathematical Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- Differential Geometry and its Applications, 2017
- Publication Type :
- Report
- Accession number :
- edsarx.1705.05818
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.difgeo.2017.09.003