2007/08/31 by Michael Forger, MICHAEL FORGER, Leandro G. Gomes +1 · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #math-ph #math.DG #math.MP #math.SG
paper · pdf · doi:10.1142/s0129055x13500189
arxiv created 2008/02/19 · openalex publication_date 2013/09/18 · arxiv updated 2014/12/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We propose new definitions of the concepts of a multisymplectic structure and of a polysymplectic structure which extend previous ones so as to cover the cases that are of interest in mathematical physics: they are tailored to apply to fiber bundles, rather than just manifolds, and at the same time they are sufficiently specific to allow us to prove Darboux theorems for the existence of canonical local coordinates. A key role is played by the notion of "symbol" of a multisymplectic form, which is a polysymplectic form representing its leading order contribution, thus clarifying the relation between these two closely related but not identical concepts.