Edge Currents and Vertex Operators for Chern-Simons Gravity

We apply elementary canonical methods for the quantization of 2+1 dimensional gravity, where the dynamics is given by E. Witten's $ISO(2,1)$ Chern-Simons action. As in a previous work, our approach does not involve choice of gauge or clever manipulations of functional integrals. Instead, we just require the Gauss law constraint for gravity to be first class and also to be everywhere differentiable. When the spatial slice is a disc, the gravitational fields can either be unconstrained or constrained at the boundary of the disc. The unconstrained fields correspond to edge currents which carry a representation of the $ISO(2,1)$ Kac-Moody algebra. Unitary representations for such an algebra have been found using the method of induced representations. In the case of constrained fields, we can classify all possible boundary conditions. For several different boundary conditions, the field content of the theory reduces precisely to that of 1+1 dimensional gravity theories. We extend the above formalism to include sources. The sources take into account self- interactions. This is done by punching holes in the disc, and erecting an $ISO(2,1)$ Kac-Moody algebra on the boundary of each hole. If the hole is originally sourceless, a source can be created via the action of a vertex operator $V$. We give an explicit expression for $V$. We shall show that when actingComment: 42 pages, UAHEP 925, SU-4240-508, INFN-NA-IV-92/1

The Chern-Simons Source as a Conformal Family and Its Vertex Operators

In a previous work, a straightforward canonical approach to the source-free quantum Chern-Simons dynamics was developed. It makes use of neither gauge conditions nor functional integrals and needs only ideas known from QCD and quantum gravity. It gives Witten's conformal edge states in a simple way when the spatial slice is a disc. Here we extend the formalism by including sources as well. The quantum states of a source with a fixed spatial location are shown to be those of a conformal family, a result also discovered first by Witten. The internal states of a source are not thus associated with just a single ray of a Hilbert space. Vertex operators for both abelian and nonabelian sources are constructed. The regularized abelian Wilson line is proved to be a vertex operator. We also argue in favor of a similar nonabelian result. The spin-statistics theorem is established for Chern-Simons dynamics even though the sources are not described by relativistic quantum fields. The proof employs geometrical methods which we find are strikingly transparent and pleasing. It is based on the research of European physicists about ``fields localized on cones.'

2+1 Einstein Gravity as a Deformed Chern-Simons Theory

The usual description of 2+1 dimensional Einstein gravity as a Chern-Simons (CS) theory is extended to a one parameter family of descriptions of 2+1 Einstein gravity. This is done by replacing the Poincare' gauge group symmetry by a q-deformed Poincare' gauge group symmetry, with the former recovered when q-> 1. As a result, we obtain a one parameter family of Hamiltonian formulations for 2+1 gravity. Although formulated in terms of noncommuting dreibeins and spin-connection fields, our expression for the action and our field equations, appropriately ordered, are identical in form to the ordinary ones. Moreover, starting with a properly defined metric tensor, the usual metric theory can be built; the Christoffel symbols and space-time curvature having the usual expressions in terms of the metric tensor, and being represented by c-numbers. In this article, we also couple the theory to particle sources, and find that these sources carry exotic angular momentum. Finally, problems related to the introduction of a cosmological constant are discussed.Comment: Latex file, 26 pages, no figure

Insulator interface effects in sputter‐deposited NbN/MgO/NbN (superconductor–insulator–superconductor) tunnel junctions

All refractory, NbN/MgO/NbN (superconductor–insulator–superconductor) tunnel junctions have been fabricated by in situ sputter deposition. The influence of MgO thickness (0.8–6.0 nm) deposited under different sputtering ambients at various deposition rates on current–voltage (I–V) characteristics of small‐area (30×30 μm) tunnel junctions is studied. The NbN/MgO/NbN trilayer is deposited in situ by dc reactive magnetron (NbN), and rf magnetron (MgO) sputtering, followed by thermal evaporation of a protective Au cap. Subsequent photolithography, reactive ion etching, planarization, and top contact (Pb/Ag) deposition completes the junction structure. Normal resistance of the junctions with MgO deposited in Ar or Ar and N2 mixture shows good exponential dependence on the MgO thickness indicating formation of a pin‐hole‐free uniform barrier layer. Further, a postdeposition in situ oxygen plasma treatment of the MgO layer increases the junction resistance sharply, and reduces the subgap leakage. A possible enrichment of the MgO layer stoichiometry by the oxygen plasma treatment is suggested. A sumgap as high as 5.7 mV is observed for such a junctio

Dual Instantons

We show how to map the Belavin-Polyakov instantons of the O(3)-nonlinear $\sigma-$model to a dual theory where they then appear as nontopological solitons. They are stationary points of the Euclidean action in the dual theory, and moreover, the dual action and the O(3)-nonlinear $\sigma-$model action agree on shell.Comment: 13 page

ON THE GEOMETRY OF THE X-RAY EMITTING REGION IN SEYFERT GALAXIES

For the first time, detailed radiative transfer calculations of Comptonized X-ray and gamma-ray radiation in a hot pair plasma above a cold accretion disk are performed using two independent codes and methods. The simulations include both energy and pair balance as well as reprocessing of the X- and gamma-rays by the cold disk. We study both plane-parallel coronae as well as active dissipation regions having shapes of hemispheres and pill boxes located on the disk surface. It is shown, contrary to earlier claims, that plane-parallel coronae in pair balance have difficulties in selfconsistently reproducing the ranges of 2-20 keV spectral slopes, high energy cutoffs, and compactnesses inferred from observations of type 1 Seyfert galaxies. Instead, the observations are consistent with the X-rays coming from a number of individual active regions located on the surface of the disk. A number of effects such as anisotropic Compton scattering, the reflection hump, feedback to the soft photon source by reprocessing, and an active region in pair equilibrium all conspire to produce the observed ranges of X-ray slopes, high energy cutoffs, and compactnesses. The spread in spectral X-ray slopes can be due to a spread in the properties of the active regions such as their compactnesses and their elevations above the disk surface. Simplified models invoking isotropic Comptonization in spherical clouds are no longer sufficient when interpreting the data.Comment: 9 pages, 3 postscript figures, figures can be obtained from the authors via e-mail: [email protected]

Organizational Design for Spill Containment in Deepwater Drilling Operations in the Gulf of Mexico: Assessment of the Marine Well Containment Company (MWCC)

The Deepwater Horizon oil spill in the Gulf of Mexico in April 2010 led to the deaths of 11 workers, a six-month moratorium on deepwater drilling in the Gulf, and nearly three months of massive engineering and logistics efforts to stop the spill. The series of failures before the well was finally capped and the spill contained revealed an inability to deal effectively with a well in deepwater and ultradeepwater. Ensuring that containment capabilities are adequate for drilling operations at these depths is therefore a salient challenge for government and industry. In this paper we assess the Marine Well Containment Company (MWCC), a consortium aimed at designing and building a system capable of containing future deepwater spills in the Gulf. We also consider alternatives for long-term readiness for deepwater spill containment. We focus on the roles of liability and regulation as determinants of readiness and the adequacy of incentives for technological innovation in oil spill containment technology to keep pace with advances in deepwater drilling capability. Liability and regulation can significantly influence the strength of these incentives. In addition, we discuss appropriate governance structure as a major determinant of the effectiveness of MWCC.oil spill, containment, industry R&D, liability, regulation, governance, innovation