Multisymplectic and polysymplectic structures on fiber bundles

Abstract

We introduce the concepts of a multisymplectic structure and a polysymplectic structure on a general fiber bundle over a general base manifold, define the concept of the symbol of a multisymplectic form, which is a polysymplectic form representing its leading order contribution, and prove Darboux theorems for the existence of canonical local coordinates.

References in corpus (3)

• The Poisson Bracket for Poisson Forms in Multisymplectic Field Theory
• Covariant Poisson Brackets in Geometric Field Theory
• Hamiltonian Multivector Fields and Poisson Forms in Multisymplectic Field Theory

Cited by in corpus (12)

• Curved space-times by crystallization of liquid fiber bundles
• Hamilton-Jacobi theory in Cauchy data space
• Vorticity and Symplecticity in Multi-Symplectic Lagrangian Gas Dynamics
• Lagrangian Distributions and Connections in Symplectic Geometry
• Quantization of Polysymplectic Manifolds
• Geometry of Lagrangian and Hamiltonian formalisms in the dynamics of strings
• Polysymplectic Reduction and the Moduli Space of Flat Connections
• De Donder-Weyl Hamiltonian formalism of MacDowell-Mansouri gravity
• Poly-Poisson Sigma models and their relational poly-symplectic groupoids
• Brackets in multicontact geometry and multisymplectization
• Poly-symplectic Geometry and the AKSZ Formalism
• Regularized polysymplectic geometry and first steps towards Floer theory for covariant field theories