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

On Fractional Tempered Stable Motion

Fractional tempered stable motion (fTSm)} is defined and studied. FTSm has the same covariance structure as fractional Brownian motion, while having tails heavier than Gaussian but lighter than stable. Moreover, in short time it is close to fractional stable L\'evy motion, while it is approximately fractional Brownian motion in long time. A series representation of fTSm is derived and used for simulation and to study some of its sample path properties.Comment: 25 pages, 6 figure

On Layered Stable Processes

Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a stable process while, in long time, it approximates another stable (possibly Gaussian) process. We also investigate the absolute continuity of a layered stable process with respect to its short time limiting stable process. A series representation of layered stable processes is derived, giving insights into both the structure of the sample paths and of the short and long time behaviors. This series is further used for sample paths simulation.Comment: 22 pages, 9 figure

Jarzynski equality for the Jepsen gas

We illustrate the Jarzynski equality on the exactly solvable model of a one-dimensional ideal gas in uniform expansion or compression. The analytical results for the probability density $P(W)$ of the work $W$ performed by the gas are compared with the results of molecular dynamics simulations for a two-dimensional dilute gas of hard spheres.Comment: 7 pages, 4 figures, submitted to Europhys. Let

Poincar\'{e} gauge theory of gravity

A Poincar\'{e} gauge theory of (2+1)-dimensional gravity is developed. Fundamental gravitational field variables are dreibein fields and Lorentz gauge potentials, and the theory is underlain with the Riemann-Cartan space-time. The most general gravitational Lagrangian density, which is at most quadratic in curvature and torsion tensors and invariant under local Lorentz transformations and under general coordinate transformations, is given. Gravitational field equations are studied in detail, and solutions of the equations for weak gravitational fields are examined for the case with a static, \lq \lq spin"less point like source. We find, among other things, the following: (1)Solutions of the vacuum Einstein equation satisfy gravitational field equations in the vacuum in this theory. (2)For a class of the parameters in the gravitational Lagrangian density, the torsion is \lq \lq frozen" at the place where \lq \lq spin" density of the source field is not vanishing. In this case, the field equation actually agrees with the Einstein equation, when the source field is \lq \lq spin"less. (3)A teleparallel theory developed in a previous paper is \lq \lq included as a solution" in a limiting case. (4)A Newtonian limit is obtainable, if the parameters in the Lagrangian density satisfy certain conditions.Comment: 27pages, RevTeX, OCU-PHYS-15

Pulse Profile Change Possibly Associated with a Glitch in an Anomalous X-Ray Pulsar 4U 0142+61

We report a glitch-like pulse frequency deviation from the simple spin-down law in an anomalous X-ray pulsar (AXP) 4U 0142+61 detected by ASCA observations. We also found a significant pulse profile change after the putative glitch. The glitch parameters resemble those found in another AXP 1RXS J170849.0$-$400910, in the Vela pulsar, and in other radio pulsars. This suggests that the radio pulsars and AXPs have the same internal structure and glitch mechanism. It must be noted, however, that the pulse frequency anomaly can also be explained by a gradual change of the spin-down rate ($\dot{P}$) without invoking a glitch.Comment: 14 pages, 4 figures, accepted by Ap

Quantum Electrodynamics at Large Distances II: Nature of the Dominant Singularities

Accurate calculations of macroscopic and mesoscopic properties in quantum electrodynamics require careful treatment of infrared divergences: standard treatments introduce spurious large-distances effects. A method for computing these properties was developed in a companion paper. That method depends upon a result obtained here about the nature of the singularities that produce the dominant large-distance behaviour. If all particles in a quantum field theory have non-zero mass then the Landau-Nakanishi diagrams give strong conditions on the singularities of the scattering functions. These conditions are severely weakened in quantum electrodynamics by effects of points where photon momenta vanish. A new kind of Landau-Nakanishi diagram is developed here. It is geared specifically to the pole-decomposition functions that dominate the macroscopic behaviour in quantum electrodynamics, and leads to strong results for these functions at points where photon momenta vanish.Comment: 40 pages, 11 encapsulated postscript figures, latexed, math_macros.tex can be found on Archive. full postscript available from http://theorl.lbl.gov/www/theorgroup/papers/35972.p

The Boundary Conformal Field Theories of the 2D Ising critical points

We present a new method to identify the Boundary Conformal Field Theories (BCFTs) describing the critical points of the Ising model on the strip. It consists in measuring the low-lying excitation energies spectra of its quantum spin chain for different boundary conditions and then to compare them with those of the different boundary conformal field theories of the $(A_2,A_3)$ minimal model.Comment: 7 pages, no figures. Talk given at the XXth International Conference on Integrable Systems and Quantum Symmetries (ISQS-20). Prague, June 201