Generalized symplectic geometry as a covering theory for the Hamiltonian theories of classical particles and fields
A covariant Hamiltonian formulation of field theories is based -- in direct generalization of the symplectic form in classical mechanics -- on a vector-valued two-form, called ``polysymplectic form''. This article uses the natural polysymplectic (``n-symplectic'') structure on frame bundles (given by the exterior derivative of the soldering form) to derive via associated bundles the polysymplectic and multisymplectic structures of Hamiltonian mechanics and field theories. Thus the frame bundle can be considered as a universal polysymplectic bundle. The construction of the symplectic structure in mechanics and the multisymplectic structure on the affine cojet bundle (as used in the ``GIMMSY'' project) are explicitly worked out.
scientific article; zbMATH DE number 951813