Spin Foam Models of Matter Coupled to Gravity

We construct a class of spin foam models describing matter coupled to gravity, such that the gravitational sector is described by the unitary irreducible representations of the appropriate symmetry group, while the matter sector is described by the finite-dimensional irreducible representations of that group. The corresponding spin foam amplitudes in the four-dimensional gravity case are expressed in terms of the spin network amplitudes for pentagrams with additional external and internal matter edges. We also give a quantum field theory formulation of the model, where the matter degrees of freedom are described by spin network fields carrying the indices from the appropriate group representation. In the non-topological Lorentzian gravity case, we argue that the matter representations should be appropriate SO(3) or SO(2) representations contained in a given Lorentz matter representation, depending on whether one wants to describe a massive or a massless matter field. The corresponding spin network amplitudes are given as multiple integrals of propagators which are matrix spherical functions.Comment: 30 pages, 9 figures, further remarks and references added. Version to appear in Class. Quant. Gra

Holography in the EPRL Model

In this research announcement, we propose a new interpretation of the EPR quantization of the BC model using a functor we call the time functor, which is the first example of a CLa-ren functor. Under the hypothesis that the universe is in the Kodama state, we construct a holographic version of the model. Generalisations to other CLa-ren functors and connections to model category theory are considered.Comment: research announcement. Latex fil

The Molecular Interstellar Medium in Ultraluminous Infrared Galaxies

We present CO observations of a large sample of ultraluminous IR galaxies out to z = 0.3. Most of the galaxies are interacting, but not completed mergers. All but one have high CO(1-0) luminosities, log(Lco [K-km/s-pc^2]) = 9.92 +/- 0.12. The dispersion in Lco is only 30%, less than that in the FIR luminosity. The integrated CO intensity correlates Strongly with the 100 micron flux density, as expected for a black body model in which the mid and far IR radiation are optically thick. We use this model to derive sizes of the FIR and CO emitting regions and the enclosed dynamical masses. Both the IR and CO emission originate in regions a few hundred parsecs in radius. The median value of Lfir/Lco = 160 Lsun/(K-km/s-pc^2), within a factor of two of the black body limit for the observed FIR temperatures. The entire ISM is a scaled up version of a normal galactic disk with densities a factor of 100 higher, making even the intercloud medium a molecular region. Using three different techniques of H2 mass estimation, we conclude that the ratio of gas mass to Lco is about a factor of four lower than for Galactic molecular clouds, but that the gas mass is a large fraction of the dynamical mass. Our analysis of CO emission reduces the H2 mass from previous estimates of 2-5e10 Msun to 0.4-1.5e10 Msun, which is in the range found for molecular gas rich spiral galaxies. A collision involving a molecular gas rich spiral could lead to an ultraluminous galaxy powered by central starbursts triggered by the compression of infalling preexisting GMC's.Comment: 34 pages LaTeX with aasms.sty, 14 Postscript figures, submitted to ApJ Higher quality versions of Figs 2a-f and 7a-c available by anonymous FTP from ftp://sbast1.ess.sunysb.edu/solomon/

Critical dynamics of diluted relaxational models coupled to a conserved density (diluted model C)

We consider the influence of quenched disorder on the relaxational critical dynamics of a system characterized by a non-conserved order parameter coupled to the diffusive dynamics of a conserved scalar density (model C). Disorder leads to model A critical dynamics in the asymptotics, however it is the effective critical behavior which is often observed in experiments and in computer simulations and this is described by the full set of dynamical equations of diluted model C. Indeed different scenarios of effective critical behavior are predicted.Comment: 4 pages, 5 figure

Discrete structures in gravity

Discrete approaches to gravity, both classical and quantum, are reviewed briefly, with emphasis on the method using piecewise-linear spaces. Models of 3-dimensional quantum gravity involving 6j-symbols are then described, and progress in generalising these models to four dimensions is discussed, as is the relationship of these models in both three and four dimensions to topological theories. Finally, the repercussions of the generalisations are explored for the original formulation of discrete gravity using edge-length variables.Comment: 30 pages, 4 figure

Radio Astronomy

Contains research objectives and reports on two research projects.National Aeronautics and Space Administration (Grant NsG-250-62)National Aeronautics and Space Administration (Grant NsG-419)U. S. Navy (Office of Naval Research) under Contract Nonr-3963(02)-Task 2Lincoln Laboratory, Purchase Order DDL BB-107U. S. Air Force under Contract AF 19(628)-50

Fractal Weyl law behavior in an open, chaotic Hamiltonian system

We numerically show fractal Weyl law behavior in an open Hamiltonian system that is described by a smooth potential and which supports numerous above-barrier resonances. This behavior holds even relatively far away from the classical limit. The complex resonance wave functions are found to be localized on the fractal classical repeller.Comment: 4 pages, 3 figures. to appear in Phys Rev

Optically Pumped NMR Measurements of the Electron Spin Polarization in GaAs Quantum Wells near Landau Level Filling Factor nu=1/3

The Knight shift of Ga-71 nuclei is measured in two different electron-doped multiple quantum well samples using optically pumped NMR. These data are the first direct measurements of the electron spin polarization, P(nu,T)=/max, near nu=1/3. The P(T) data at nu=1/3 probe the neutral spin-flip excitations of a fractional quantum Hall ferromagnet. In addition, the saturated P(nu) drops on either side of nu=1/3, even in a Btot=12 Tesla field. The observed depolarization is quite small, consistent with an average of about 0.1 spin-flips per quasihole (or quasiparticle), a value which does not appear to be explicable by the current theoretical understanding of the FQHE near nu=1/3.Comment: 4 pages (REVTEX), 5 eps figures embedded in text; minor changes, published versio