Unconstrained variational principle and canonical structure for relativistic elasticity

A description of relativistic elasticity based on a parametrization of material configurations in terms of unconstrained degrees of freedom is proposed. In this description elasticity may be treated as a gauge-type theory, where the role of gauge transformations is played by the diffeomorphisms of the material space. It is shown that the dynamics of the theory may be formulated in terms of three independent, hyperbolic, second-order partial differential equations imposed on three independent gauge potentials. The corresponding unconstrained variational principle is given. The equality between the canonical and the symmetric energy-momentum tensors (Rosenfeld-Belinfante theorem) is proved and the equivalence with existing formulations of the theory is discussed. The canonical (unconstrained) momenta conjugate to the three configuration variables and the Hamiltonian of the system are found.