On stress-energy tensors

Abstract

An old but not well-known formal method is detailed and used to obtain the symmetrized stress-energy tensor from Noether's theorem applied to Poincaré-covariant Lagrangian field theories. A variation in a standard method is presented and used to obtain the corresponding canonical stress-energy tensor, valid in arbitrary curvilinear coordinates, in the limit of Lorentz metric. These two tensors are shown to be equal, in each case, for scalar, Maxwell, Dirac spinor, coupled Maxwell-Dirac, and vector (non-Maxwell) Lagrangian field theories.