In the $\bar{ \mbox{ \rm Poincar\'{ e}}}$ 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 Poincar\'{ e} group as the structure group, we examine the tensorial properties of the dynamical energy-momentum density ${ }^{ G}{ \mathbf T}_{ k}{ }^{ \mu}$ and the ` ` spin" angular momentum density ${ }^{ G}{ \mathbf S}_{ kl}{ }^{ \mu}$ of the gravitational field. They are both space-time vector densities, and transform as tensors under { \em global} $SL(2,C)$- transformations. Under { \em local} internal translation, ${ }^{ G}{ \mathbf T}_{ k}{ }^{ \mu}$ is invariant, while ${ }^{ G}{ \mathbf S}_{ kl}{ }^{ \mu}$ transforms inhomogeneously. The dynamical energy-momentum density ${ }^{ M}{ \mathbf T}_{ k}{ }^{ \mu}$ and the ` ` spin" angular momentum density ${ }^{ M}{ \mathbf S}_{ kl}{ }^{ \mu}$ 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 $\bar{ \mbox{ \rm Poincar\'{ e}}}$ gauge transformations. The corresponding discussions in extended new general relativity which is obtained as a teleparallel limit of $\bar{ \mbox{ \rm Poincar\'{ e}}}$ 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. In both theories, integrations of these densities on a space-like surface give the total energy-momentum and { \em total} (={ \em spin}+{ \em orbital}) angular momentum for asymptotically flat space-time. The tensorial properties of canonical energy-momentum and ` ` extended orbital angular momentum" densities are also examined.
Categories: gr-qc