Geometry of the transport equation in multicomponent WKB approximations
Although the WKB approximation for multicomponent systems has been intensively studied in the literature, its geometric and global aspects are much less well understood than in the scalar case. In this paper we give a completely geometric derivation of the transport equation, without using local sections and without assuming complete diagonalizability of the matrix valued principal symbol, or triviality of its eigenbundles. The term (unnamed in the previous literature) appearing in the transport equation in addition to the covariant derivative with respect to a natural projected connection is a tensor, independent of the choice of any sections. We give a goemetric interpretation of this tensor, involving the contraction of the curvature of the eigenbundle and an analog of the second fundamental form with the Poisson tensor in phase space. In the non-degenerate case this term may be rewritten in an even simpler geometric form. Finally, we discuss obstructions to the existence of WKB states and give a geometric description of the quantization condition for WKB states for a non-degenerate eigenvalue-function.

title: Classical Theta Functions and Quantum Tori
abstract: The Schwartz kernel of the multiplication operation on a quantum torus is shown to be the distributional boundary value of a classical multivariate theta function. The kernel satisfies a Schrodinger equation in which the role of time is played by the deformation parameter 11 and the role of the hamiltonian by a Poisson structure. At least in some special cases, the kernel can be written as a sum of products of single variable theta functions. A quantum torus is, by definition, a "space" whose (noncommutative) algebra of functions is obtained by deformation of the (commutative) algebra of functions on a torus (R/Zy. In this note, we observe that the Schwartz kernels of the multiplication operators for a class of quantum tori are the (distributional) boundary values of classical theta functions, and we draw some conclusions from this observation. In particular, we show that each of these kernels satisfies a Schrodinger equation, in which the role of time is played by the deformation parameter h, and the role of the hamiltonian is played by the Poisson structure associated with the deformation. Thus, the "evolution in Plank's constant" of a torus is like the time evolution of a free particle, with the initial state (the Schwartz kernel of the operator of pointwise multiplication) being a delta function, like the initial state of a particle with certain position and totally uncertain momentum. This evolution equation suggests a possible answer to the question of how a deformed product must behave after the deformation parameter h has left the first infinitesimal neighborhood of zero. We note that our work seems to be quite different from Manin's study  of quantum theta functions, which are special functions on the quantum tori themselves. Communicated by T. Kawai, September 13, 1993.  Research partially supported by NSF Grant DMS-93-09653.

title: Hopfish structure and modules over irrational rotation algebras
abstract: Inspired by the group structure on $S^1/ \bbZ$, we introduce a weak hopfish structure on an irrational rotation algebra $A$ of finite Fourier series. We consider a class of simple $A$-modules defined by invertible elements, and we compute the tensor product between these modules defined by the hopfish structure. This class of simple modules turns out to generate an interesting commutative unital ring.

title: Noncommutative Geometry and Geometric Quantization

title: Reduction and quantization for singular momentum mappings
abstract: When a Hamiltonian action of Lie group on a symplectic manifold has a singular momentum mapping, the reduced manifold may not exist. Nevertheless, we may always construct a Poisson algebra which corresponds to the functions on the reduced manifold in the regular case. The ideas of geometric quantization are extended to Poisson algebras, and it is shown in an example that quantization may be carried out before or after reduction, with isomorphic results.

title: Courant Algebroids and Strongly Homotopy Lie Algebras
abstract: Courant algebroids are structures which include as examples the doubles of Lie bialgebras and the direct sum of tangent and cotangent bundles with the bracket introduced by T. Courant for the study of Dirac structures. Within the category of Courant algebroids one can construct the doubles of Lie bialgebroids, the infinitesimal objects for Poisson groupoids. We show that Courant algebroids can be considered as strongly homotopy Lie algebras.

title: Evidence for long-term gamma-ray and x-ray variability from the unidentified TeV source HESS J0632+057
abstract: HESS J0632+057 is one of only two unidentified very-high-energy gamma-ray sources which appear to be point-like within experimental resolution. It is possibly associated with the massive Be star MWC 148 and has been suggested to resemble known TeV binary systems like LS I +61 303 or LS 5039. HESS J0632+057 was observed by VERITAS for 31 hr in 2006, 2008, and 2009. During these observations, no significant signal in gamma rays with energies above 1?TeV was detected from the direction of HESS J0632+057. A flux upper limit corresponding to 1.1% of the flux of the Crab Nebula has been derived from the VERITAS data. The nondetection by VERITAS excludes with a probability of 99.993% that HESS J0632+057 is a steady gamma-ray emitter. Contemporaneous X-ray observations with the Swift X-Ray Telescope reveal a factor of 1.8 ? 0.4 higher flux in the 1-10?keV range than earlier X-ray observations of HESS J0632+057. The variability in the gamma-ray and X-ray fluxes supports interpretation of the object as a gamma-ray emitting binary.

title: Searches for periodic gravitational waves from unknown isolated sources and Scorpius X-1: Results from the second LIGO science run
abstract: We carry out two searches for periodic gravitational waves using the most sensitive few hours of data from the second LIGO science run. Both searches exploit fully coherent matched filtering and cover wide areas of parameter space, an innovation over previous analyses which requires considerable algorithm development and computational power. The first search is targeted at isolated, previously unknown neutron stars, covers the entire sky in the frequency band 160–728.8 Hz, and assumes a frequency derivative of less than 4×10^(−10)  Hz/s. The second search targets the accreting neutron star in the low-mass x-ray binary Scorpius X-1 and covers the frequency bands 464–484 Hz and 604–624 Hz as well as the two relevant binary orbit parameters. Because of the high computational cost of these searches we limit the analyses to the most sensitive 10 hours and 6 hours of data, respectively. Given the limited sensitivity and duration of the analyzed data set, we do not attempt deep follow-up studies. Rather we concentrate on demonstrating the data analysis method on a real data set and present our results as upper limits over large volumes of the parameter space. In order to achieve this, we look for coincidences in parameter space between the Livingston and Hanford 4-km interferometers. For isolated neutron stars our 95% confidence level upper limits on the gravitational wave strain amplitude range from 6.6×10^(−23) to 1×10^(−21) across the frequency band; for Scorpius X-1 they range from 1.7×10^(−22) to 1.3×10^(−21) across the two 20-Hz frequency bands. The upper limits presented in this paper are the first broadband wide parameter space upper limits on periodic gravitational waves from coherent search techniques. The methods developed here lay the foundations for upcoming hierarchical searches of more sensitive data which may detect astrophysical signals.

title: A Search for Dark Matter Annihilation with the Whipple 10 m Telescope
abstract: We present observations of the dwarf galaxies Draco and Ursa Minor, the Local Group galaxies M32 and M33, and the globular cluster M15 conducted with the Whipple 10 m gamma-ray telescope to search for the gamma-ray signature of self-annihilating weakly interacting massive particles (WIMPs), which may constitute astrophysical dark matter (DM). We review the motivations for selecting these sources based on their unique astrophysical environments and report the results of the data analysis that produced upper limits on the excess rate of gamma rays for each source. We consider models for the DM distribution in each source based on the available observational constraints and discuss possible scenarios for the enhancement of the gamma-ray luminosity. Limits on the thermally averaged product of the total self-annihilation cross section and velocity of the WIMP, -->?? , are derived using conservative estimates for the magnitude of the astrophysical contribution to the gamma-ray flux. Although these limits do not constrain predictions from the currently favored theoretical models of supersymmetry (SUSY), future observations with VERITAS will probe a larger region of the WIMP parameter phase space, -->?? , and WIMP particle mass ( -->m?).

title: Results from the first two years of VERITAS observations
abstract: The VERITAS observatory is an imaging atmospheric Cherenkov telescope array located in southern Arizona and covers an energy range between 100 GeV and 30 TeV. The VERITAS collaboration pursues a rigorous observing program that targets a range of key science objectives in astrophysics and particle physics; the understanding of the origin of cosmic rays, the search for supersymmetric dark matter self-annihilation, illuminating the connection between black holes and relativistic jets and constraints to the cosmological diffuse infrared background. We provide a summary of results from the first two years of observations with the full 4-telecope array reported at RICAP09.

title: Measurements of exclusive semileptonic decays of D mesons
abstract: Using a sample of integrated luminosity 1.68 fb −1 collected with the CLEO-II detector at the Cornell Electron Storage Ring, we measure the branching ratios for the dominant exclusive semileptonic decays D → K l ν and D → K ∗ l ν , using charged and neutral D mesons. We also make a precise measurement of the vector form factor for the decay D 0 → K − l + ν , using a sample of 2700 events.