Energy-momentum and angular momentum densities in gauge theories of gravity

In the Poincare gauge theory of gravity, which has been formulated on the basis of a principal fiber bundle over the space-time manifold having the covering group of the proper orthochronous Poincare group as the structure group, we examine the tensorial properties of the dynamical energy-momentum density T-G(k)mu and the "spin" angular momentum density S-G(ki)mu of the gravitational field. They are both space-time vector densities, and transform as tensors under global SL(2,C) transformations. Under local internal translation, T-G(k)mu is invariant, while S-G(ki)mu transforms inhomogeneously. The dynamical energy-momentum density T-M(k)mu and the "spin" angular momentum density S-M(ki)mu of the matter field are also examined, and they are known to be space-time vector densities and to obey tensorial transformation rules under internal Poincare gauge transformations. The corresponding discussions in extended new general relativity which is obtained as a teleparallel limit of Poincare gauge theory are also given, and energy-momentum and "spin" angular momentum densities are known to be well behaved. Namely, they are all space-time vector densities, etc. The tensorial properties of canonical energy-momentum and "extended orbital angular momentum'' densities are also examined.