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

Performance of single photon-counting X-ray charge coupled devices

Results of intial performance tests on X-ray sensing properties of charge-coupled devices (CCDs) are presented. CCDs have demonstrated excellent spatial resolution and good spectral resolution, superior to that of non-imaging proportional counters

Constraints on the equation of state of dark energy and the Hubble constant from stellar ages and the CMB

We place tight constraints on the redshift-averaged, effective value of the equation of state of dark energy, w, using only the absolute ages of Galactic stars and the observed position of the first peak in the angular power spectrum of the CMB. We find w<-0.8 at the 68% confidence level. If we further consider that w > -1, this finding suggests that within our uncertainties, dark energy is indistinguishable from a classical vacuum energy term. We detect a correlation between the ages of the oldest galaxies and their redshift. This opens up the possibility of measuring w(z) by computing the relative ages of the oldest galaxies in the universe as a function of redshift, dz/dt. We show that this is a realistic possibility by computing dz/dt at z~0 from SDSS galaxies and obtain an independent estimate for the Hubble constant, H_0 = 69 \pm 12 km s-1 Mpc-1. The small number of galaxies considered at z>0.2 does not yield, currently, a precise determination of w(z), but shows that the age--redshift relation is consistent with a Standard LCDM universe with $w=-1$.Comment: Submitted to Ap

Current Algebra and Conformal Field Theory on a Figure Eight

We examine the dynamics of a free massless scalar field on a figure eight network. Upon requiring the scalar field to have a well defined value at the junction of the network, it is seen that the conserved currents of the theory satisfy Kirchhoff's law, that is that the current flowing into the junction equals the current flowing out. We obtain the corresponding current algebra and show that, unlike on a circle, the left- and right-moving currents on the figure eight do not in general commute in quantum theory. Since a free scalar field theory on a one dimensional spatial manifold exhibits conformal symmetry, it is natural to ask whether an analogous symmetry can be defined for the figure eight. We find that, unlike in the case of a manifold, the action plus boundary conditions for the network are not invariant under separate conformal transformations associated with left- and right-movers. Instead, the system is, at best, invariant under only a single set of transformations. Its conserved current is also found to satisfy Kirchhoff's law at the junction. We obtain the associated conserved charges, and show that they generate a Virasoro algebra. Its conformal anomaly (central charge) is computed for special values of the parameters characterizing the network.Comment: 39 pages; Latex with 1 figure included in encapsulated postscript format. psbox.tex require

‘‘There’s so much more to it than what I initially thought’’: Stepping into researchers’ shoes with a class activity in a first year psychology survey course

In psychology, it is widely agreed that research methods, although central to the discipline, are particularly challenging to learn and teach, particularly at introductory level. This pilot study explored the potential of embedding a student-conducted research activity in a one-semester undergraduate Introduction to Psychology survey course, with the aims of (a) engaging students with the topic of research methods; (b) developing students’ comprehension and application of research methods concepts; and (c) building students’ ability to link research with theory. The research activity explored shoe ownership, examining gender differences and relationships with age, and linking to theories of gender difference and of consumer identity. The process of carrying out the research and reflecting on it created a contextualized, active learning environment in which students themselves raised many issues that research methods lectures seek to cover. Students also wrote richer assignments than standard first year mid-term essay

Report of the panel on lithospheric structure and evolution, section 3

The panel concluded that NASA can contribute to developing a refined understanding of the compositional, structural, and thermal differences between continental and oceanic lithosphere through a vigorous program in solid Earth science with the following objectives: determine the most fundamental geophysical property of the planet; determine the global gravity field to an accuracy of a few milliGals at wavelengths of 100 km or less; determine the global lithospheric magnetic field to a few nanoTeslas at a wavelength of 100 km; determine how the lithosphere has evolved to its present state via acquiring geologic remote sensing data over all the continents