GENERALIZED SYMPLECTIC-GEOMETRY AS A COVERING THEORY FOR THE HAMILTONIAN THEORIES OF CLASSICAL PARTICLES AND FIELDS

It is shown that the symplectic potentials which underlie the symplect ic geometry of classical particles and the multisymplectic geometry of classical fields are obtained as projections of a generalized symplec tic potential defined on appropriate bundles of frames on a certain ma nifold. In this sense generalized symplectic geometry is a covering th eory for Hamiltonian theories of both particles and fields.