A Frame Bundle Generalization of Multisymplectic Momentum Mappings

We construct momentum mappings for covariant Hamiltonian field theories using a generalization of symplectic geometry to the bundle LV Y of vertically adapted linear frames over the bundle of field configurations Y . Field momentum observables are vector-valued momentum mappings generated from automorphisms of Y , using the (n + k)-symplectic geometry of LV Y . These momentum observables on LV Y generalize those in covariant multisymplectic geometry and produce conserved field quantities along flows. Three examples illustrate the utility of these momentum mappings: orthogonal symmetry of a Kaluza-Klein theory generates the conservation of field angular momentum, affine reparametrization symmetry in time-evolution mechanics produces a version of the parallel axis theorem of rotational dynamics, and time reparametrization symmetry in time-evolution mechanics gives us an improvement upon a parallel transport law.