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

Gotay, M. J. and J. E., Marsden

Contemp. Math., (1992) 132, 367-392

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 $\cal {T}$^$\mu$_$\nu$ that we construct is defined using the (multi)momentum map associated to the spacetime diffeomorphism group. The tensor $\cal {T}$^$\mu$_$\nu$ 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 $\cal {T}$^$\mu$_$\nu$ coincides with the Hilbert tensor and hence is automatically symmetric.