An invitation to multisymplectic geometry

Understand

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 wether 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.