Stress-Energy-Momentum Tensors and the Belinfante-Rosenfeld Formula

Abstract

We present a new method of constructing a stress-energy-momentum tensor for a classical field theory based on covariance considerations and Noether theory. The stress-energy-momentum tensor T ^μ _ν that we construct is defined using the (multi)momentum map associated to the spacetime diffeomorphism group. The tensor T ^μ _ν is uniquely determined as well as gauge-covariant, and depends only upon the divergence equivalence class of the Lagrangian. It satisfies a generalized version of the classical Belinfante-Rosenfeld formula, and hence naturally incorporates both the canonical stress-energy-momentum tensor and the “correction terms” that are necessary to make the latter well behaved. Furthermore, in the presence of a metric on spacetime, our T^(μν) coincides with the Hilbert tensor and hence is automatically symmetric.