48 research outputs found
Link Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory
We define and study the properties of observables associated to any link in
(where is a compact surface) using the
combinatorial quantization of hamiltonian Chern-Simons theory. These
observables are traces of holonomies in a non commutative Yang-Mills theory
where the gauge symmetry is ensured by a quantum group. We show that these
observables are link invariants taking values in a non commutative algebra, the
so called Moduli Algebra. When these link invariants are pure
numbers and are equal to Reshetikhin-Turaev link invariants.Comment: 39, latex, 7 figure
Combinatorial expression for universal Vassiliev link invariant
The most general R-matrix type state sum model for link invariants is
constructed. It contains in itself all R-matrix invariants and is a generating
function for "universal" Vassiliev link invariants. This expression is more
simple than Kontsevich's expression for the same quantity, because it is
defined combinatorially and does not contain any integrals, except for an
expression for "the universal Drinfeld's associator".Comment: 20 page
Graph Invariants of Vassiliev Type and Application to 4D Quantum Gravity
We consider a special class of Kauffman's graph invariants of rigid vertex
isotopy (graph invariants of Vassiliev type). They are given by a functor from
a category of colored and oriented graphs embedded into a 3-space to a category
of representations of the quasi-triangular ribbon Hopf algebra . Coefficients in expansions of them with respect to () are
known as the Vassiliev invariants of finite type. In the present paper, we
construct two types of tangle operators of vertices. One of them corresponds to
a Casimir operator insertion at a transverse double point of Wilson loops. This
paper proposes a non-perturbative generalization of Kauffman's recent result
based on a perturbative analysis of the Chern-Simons quantum field theory. As a
result, a quantum group analog of Penrose's spin network is established taking
into account of the orientation. We also deal with the 4-dimensional canonical
quantum gravity of Ashtekar. It is verified that the graph invariants of
Vassiliev type are compatible with constraints of the quantum gravity in the
loop space representation of Rovelli and Smolin.Comment: 34 pages, AMS-LaTeX, no figures,The proof of thm.5.1 has been
improve
Very-high energy gamma-ray astronomy: A 23-year success story in high-energy astroparticle physics
Very-high energy (VHE) gamma quanta contribute only a minuscule fraction -
below one per million - to the flux of cosmic rays. Nevertheless, being neutral
particles they are currently the best "messengers" of processes from the
relativistic/ultra-relativistic Universe because they can be extrapolated back
to their origin. The window of VHE gamma rays was opened only in 1989 by the
Whipple collaboration, reporting the observation of TeV gamma rays from the
Crab nebula. After a slow start, this new field of research is now rapidly
expanding with the discovery of more than 150 VHE gamma-ray emitting sources.
Progress is intimately related with the steady improvement of detectors and
rapidly increasing computing power. We give an overview of the early attempts
before and around 1989 and the progress after the pioneering work of the
Whipple collaboration. The main focus of this article is on the development of
experimental techniques for Earth-bound gamma-ray detectors; consequently, more
emphasis is given to those experiments that made an initial breakthrough rather
than to the successors which often had and have a similar (sometimes even
higher) scientific output as the pioneering experiments. The considered energy
threshold is about 30 GeV. At lower energies, observations can presently only
be performed with balloon or satellite-borne detectors. Irrespective of the
stormy experimental progress, the success story could not have been called a
success story without a broad scientific output. Therefore we conclude this
article with a summary of the scientific rationales and main results achieved
over the last two decades.Comment: 45 pages, 38 figures, review prepared for EPJ-H special issue "Cosmic
rays, gamma rays and neutrinos: A survey of 100 years of research
A magic connection between massive and massless diagrams
A useful connection between two-loop massive vacuum integrals and one-loop
off-shell triangle diagrams with massless internal particles is established for
arbitrary values of the space-time dimension n.Comment: 11 pages, plain latex, 1 figure (in latex); ps file available by
anonymous ftp at ftp://vsfys1.fi.uib.no/anonymous/pub/bergen95-07.p
Multiwavelength observations of a TeV-Flare from W comae
We report results from an intensive multiwavelength campaign on the intermediate-frequency-peaked BL Lacertae object W Com (z = 0.102) during a strong outburst of very high energy gamma-ray emission in 2008 June. The very high energy gamma-ray signal was detected by VERITAS on 2008 June 7-8 with a flux F(>200 GeV) =(5.7 0.6) × 10-11 cm-2 s -1, about three times brighter than during the discovery of gamma-ray emission from W Com by VERITAS in 2008 March. The initial detection of this flare by VERITAS at energies above 200 GeV was followed by observations in high-energy gamma rays (AGILE; E γ≥ 100 MeV), X-rays (Swift and XMM-Newton), and at UV, and ground-based optical and radio monitoring through the GASP-WEBT consortium and other observatories. Here we describe the multiwavelength data and derive the spectral energy distribution of the source from contemporaneous data taken throughout the flare. © 2009. The American Astronomical Society. All rights reserved
The Great Markarian 421 Flare of 2010 February: Multiwavelength Variability and Correlation Studies
We report on variability and correlation studies using multiwavelength observations of the blazar Mrk 421 during the month of 2010 February, when an extraordinary flare reaching a level of ∼27 Crab Units above 1 TeV was measured in very high energy (VHE) γ-rays with the Very Energetic Radiation Imaging Telescope Array System (VERITAS) observatory. This is the highest flux state for Mrk 421 ever observed in VHE γ-rays. Data are analyzed from a coordinated campaign across multiple instruments, including VHE γ-ray (VERITAS, Major Atmospheric Gamma-ray Imaging Cherenkov), high-energy γ-ray (Fermi-LAT), X-ray (Swift, Rossi X-ray Timing Experiment, MAXI), optical (including the GASP-WEBT collaboration and polarization data), and radio (Metsahovi, Owens Valley Radio Observatory, University of Michigan Radio Astronomy Observatory). Light curves are produced spanning multiple days before and after the peak of the VHE flare, including over several flare "decline" epochs. The main flare statistics allow 2 minute time bins to be constructed in both the VHE and optical bands enabling a cross-correlation analysis that shows evidence for an optical lag of ∼25-55 minutes, the first time-lagged correlation between these bands reported on such short timescales. Limits on the Doppler factor (δ ⪆ 33) and the size of the emission region (δ-1RB≲ 3.8 × 1013cm) are obtained from the fast variability observed by VERITAS during the main flare. Analysis of 10 minute binned VHE and X-ray data over the decline epochs shows an extraordinary range of behavior in the flux-flux relationship, from linear to quadratic to lack of correlation to anticorrelation. Taken together, these detailed observations of an unprecedented flare seen in Mrk 421 are difficult to explain with the classic single-zone synchrotron self-Compton model.</p