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

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.Comment: 18 page

Quantum Electrodynamics at Large Distances III: Verification of Pole Factorization and the Correspondence Principle

In two companion papers it was shown how to separate out from a scattering function in quantum electrodynamics a distinguished part that meets the correspondence-principle and pole-factorization requirements. The integrals that define the terms of the remainder are here shown to have singularities on the pertinent Landau singularity surface that are weaker than those of the distinguished part. These remainder terms therefore vanish, relative to the distinguished term, in the appropriate macroscopic limits. This shows, in each order of the perturbative expansion, that quantum electrodynamics does indeed satisfy the pole-factorization and correspondence-principle requirements in the case treated here. It also demonstrates the efficacy of the computational techniques developed here to calculate the consequences of the principles of quantum electrodynamics in the macroscopic and mesoscopic regimes.Comment: latex, 39 pages, 2 Figures included as uuencoded, tarred, gzipped, encapsulated postscript files, uses math_macros.te

String and Vortex

We discuss how the geometry of $D2$-$D0$ branes may be related to Gromov-Witten theory of Calabi-Yau threefolds.Comment: 31 page

Exotic black hole solution in teleparallel theory of (2+1)-dimensional gravity

A black hole solution in a teleparallel theory of (2+1)-dimensional gravity, given in a previous paper, is examined. This solution is also a solution of the three-dimensional vacuum Einstein equation with a vanishing cosmological constant. Remarkable is the fact that this solution gives a black hole in a \lq \lq flat-land" in the Einstein theory and a Newtonian limit. Coordinate transformations to \lq \lq Minkowskian" coordinates, however, are singular not only at the origin, but also on the event horizon. {\em In the three-dimensional Einstein theory, vacuum regions of space-times can be locally non-trivial}.Comment: 11, ReVTe