An invitation to multisymplectic geometry

Abstract In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we reformulate the latter in “multisymplectic terms”. Furthermore, we investigate basic questions on normal forms of multisymplectic manifolds, notably the questions whether and when Darboux-type theorems hold, and “how many” diffeomorphisms certain, important classes of multisymplectic manifolds possess. Finally, we survey recent advances in the area of symmetries and conserved quantities on multisymplectic manifolds.

• Publication year

  2018

• Venue

  Journal of Geometry and Physics

• Publication date

  2018-04-07

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1016/j.geomphys.2019.03.006arXiv 1804.02553
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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