Stress-Energy-Momentum Tensors
and the Belinfante-Rosenfeld Formula
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 Tνµ that we construct
is defined using the (multi)momentum map associated to the spacetime
diffeomorphism group. The tensor Tνµ
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 Tνµ coincides with the
Hilbert tensor and hence is automatically symmetric.
This is joint work with Jerrold E. Marsden.