Quantum Holonomies in (2+1)-Dimensional Gravity

We describe an approach to the quantisation of (2+1)-dimensional gravity with topology R x T^2 and negative cosmological constant, which uses two quantum holonomy matrices satisfying a q-commutation relation. Solutions of diagonal and upper-triangular form are constructed, which in the latter case exhibit additional, non-trivial internal relations for each holonomy matrix. Representations are constructed and a group of transformations - a quasi-modular group - which preserves this structure, is presented.Comment: 10 pages Latex no figure

Invariants of 2+1 Quantum Gravity

In [1,2] we established and discussed the algebra of observables for 2+1 gravity at both the classical and quantum level. Here our treatment broadens and extends previous results to any genus $g$ with a systematic discussion of the centre of the algebra. The reduction of the number of independent observables to $6g-6 (g > 1)$ is treated in detail with a precise classification for $g = 1$ and $g = 2$.Comment: 10 pages, plain TEX, no figures, DFTT 46/9

Use of W-Boson Longitudinal-Transverse Interference in Top Quark Spin-Correlation Functions: II

This continuation of the derivation of general beam-referenced stage-two spin-correlation functions is for the analysis of top-antitop pair-production at the Tevatron and at the Large Hadron Collider. Both the gluon-production and the quark-production contributions are included for the charged-lepton-plus-jets reaction p p or p bar{p} --> t bar{t} --> (W^+ b)(W^- bar{b}) --> (l^{+} nu b)(W^- bar{b}). There is a simple 4-angle beam-referenced spin-correlation function for determination of the relative sign of, or for measurement of a possible non-trivial phase between the two dominant helicity amplitudes for t --> W^{+} b decay. There is an analogous function and tests for bar{t} --> W^{-} bar{b} decay. This signature requires use of the (t bar{t}) c.m.-energy of the hadronically decaying W-boson, or the kinematically equivalent cosine of the polar-angle of W-boson emission in the anti-top (top) decay frame. Spinors and their outer-products are constructed so that the helicity-amplitude phase convention of Jacob & Wick can be used throughout for the fixing of the signs associated with this large W-boson longitudinal-transverse interference effect.Comment: Continuation of hep-ph/0506240 to include gluon-production contribution; 3 "postscript" figures. Equation numbers as in published-on-line EPJ

A hydrodynamic approach to the Bose-Glass transition

Nonlinear hydrodynamics is used to evaluate disorder-induced corrections to the vortex liquid tilt modulus for finite screening length and arbitrary disorder geometry. Explicit results for aligned columnar defects yield a criterion for locating the Bose glass transition line at all fields.Comment: 8 pages, 2 figures. Contributed talk at the First ESF-Vortex Matter Conference in Agia Pelagia, Crete, September 199

Quantum geometry from 2+1 AdS quantum gravity on the torus

Wilson observables for 2+1 quantum gravity with negative cosmological constant, when the spatial manifold is a torus, exhibit several novel features: signed area phases relate the observables assigned to homotopic loops, and their commutators describe loop intersections, with properties that are not yet fully understood. We describe progress in our study of this bracket, which can be interpreted as a q-deformed Goldman bracket, and provide a geometrical interpretation in terms of a quantum version of Pick's formula for the area of a polygon with integer vertices.Comment: 19 pages, 11 figures, revised with more explanations, improved figures and extra figures. To appear GER

On the possibility of Dark Energy from corrections to the Wheeler-De Witt equation

We present a method for approximating the effective consequence of generic quantum gravity corrections to the Wheeler-DeWitt equation. We show that in many cases these corrections can produce departures from classical physics at large scales and that this behaviour can be interpreted as additional matter components. This opens up the possibility that dark energy (and possible dark matter) could be large scale manifestations of quantum gravity corrections to classical general relativity. As a specific example we examine the first order corrections to the Wheeler-De Witt equation arising from loop quantum cosmology in the absence of lattice refinement and show how the ultimate breakdown in large scale physics occurs.Comment: 4 pages, 1 figure. Minor modifications to match version to appear in Phys. Let.

Semiquandles and flat virtual knots

We introduce an algebraic structure we call semiquandles whose axioms are derived from flat Reidemeister moves. Finite semiquandles have associated counting invariants and enhanced invariants defined for flat virtual knots and links. We also introduce singular semiquandles and virtual singular semiquandles which define invariants of flat singular virtual knots and links. As an application, we use semiquandle invariants to compare two Vassiliev invariants.Comment: 14 page

Stellar Absorption Lines in the Spectra of Seyfert Galaxies

We have measured the strengths of Ca II Triplet and Mgb stellar absorption lines in the nuclear and off-nuclear spectra of Seyfert galaxies. These features are diluted to varying degrees by continuum emission from the active nucleus and from young stars. Ca II Triplet strengths can be enhanced if late-type supergiant stars dominate the near-IR light. Thus, objects with strong Ca II Triplet and weak Mgb lines may be objects with strong bursts of star formation. We find that for most of our sample the line strengths are at least consistent with dilution of a normal galaxy spectrum by a power law continuum, in accord with the standard model for AGN. However, for several Seyferts in our sample, it appears that dilution by a power law continuum cannot simultaneously explain strong Ca II Triplet and relatively weak Mgb. Also, these objects occupy the region of the IRAS color-color diagram characteristic of starburst galaxies. In these objects it appears that the optical to near-IR emission is dominated by late-type supergiants produced in a circumnuclear burst of star formation.Comment: 4 pages, 3 figures, to appear in Advances in Space Research, presented at "The AGN/Host Galaxy Connection" as part of the Scientific Assembly of COSPAR, July 12-18 Nagoya, Japa

In Memory of the Holocaust: We Have Come a Long Way

Sermon delivered at the 18th Annual Christian Service in Memory of the Holocaust, St Peter\u27s (Erindale) Anglican Church, Mississauga, Ont, April 26, 1998