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arXiv · 1610.08689

Variational principles and symmetries on fibered multisymplectic manifolds

Jordi Gaset·Pedro D. Prieto-Martínez·Narciso Román-Roy
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Abstract

The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes, as special cases, first and higher order field theories and (non-autonomous) mechanics.

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Jordi Gaset, Pedro D. Prieto-Martínez, Narciso Román-Roy. 2016-10-27. Variational principles and symmetries on fibered multisymplectic manifolds. https://arxiv.org/abs/1610.08689

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