Dynamics of tensor fields in hyperspace. III

The dynamics of tensor fields with derivative gravitational coupling on a given Riemannian background is formulated as Hamiltonian dynamics of hypersurface projections of these fields propagating in hyperspace. The first-order spacetime action is transformed into an equivalent hypersurface form. The supermomentum and different parts of the super-Hamiltonian are identified with projected pieces of the (symmetrical, canonical, and spin) energy–momentum tensors, and their kinematical and dynamical roles are analyzed. Hypersurface variables are included among the canonical variables, and the resulting first-order generalized Hamiltonian dynamics of hypertensor fields is discussed. The closing relations for the constraint functions in the generalized Hamiltonian dynamics are derived from the foliation independence of the hypersurface action. The elimination of the λ-multipliers, which are characteristic to the first-order theory, is accomplished. The general formalism is specialized to the n-form fields with nonderivative gravitational coupling.