On the energy-momentum tensor

Abstract

We clarify the relation among canonical, metric and Belinfante's energy-momentum tensors for general tensor field theories. For any tensor field T, we define a new tensor field T̃ in terms of which metric and Belinfante's energy-momentum tensors are readily computed. We show that the latter is the one that arises naturally from Noether's theorem for an arbitrary spacetime and it coincides on-shell with the metric one.