Lorentz invariance, momentum-energy tensors, and the MHD problem
A Memorandum with a threefold purpose. First, the rigorous consequences of Lorentz invariance for arbitrary tensor fields are obtained. Second, under a precise definition of the momentum-energy tensor, a system of equations for the determination of this tensor in terms of the energy density T00, and a system of equations for the determination of the arguments of T00 are obtained. A formulation of M H D problems is then given and is shown to be well set. This is accomplished by means of an extension of the classical existence theorems for linear partial differential equations whereby a collection of state variables can be said to be complete. Lastly, an alternative formulation is presented in which the momentum-energy tensor is derived from the equations of motion and a variational principle. The latter corresponds to the Lagrangian approach to field theory, while the presentation in terms of Lorentz invariance and the generation of the momentum-energy tensor from T00 corresponds to the Hamiltonian approach. 47 pp. Bibliog.