Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j3j Symbols, and Character Localization

In this paper we employ a novel technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index $J$) of generic Wigner matrix elements $D^{J}_{MM'}(g)$. We use this result to derive asymptotic formulae for the character $\chi^J(g)$ of an SU(2) group element and for Wigner's $3j$ symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for $\chi^J(g)$ is in fact exact. This result provides a non trivial example of a Duistermaat-Heckman like localization property for discrete sums.Comment: 36 pages, 3 figure

A New Recursion Relation for the 6j-Symbol

The 6j-symbol is a fundamental object from the re-coupling theory of SU(2) representations. In the limit of large angular momenta, its asymptotics is known to be described by the geometry of a tetrahedron with quantized lengths. This article presents a new recursion formula for the square of the 6j-symbol. In the asymptotic regime, the new recursion is shown to characterize the closure of the relevant tetrahedron. Since the 6j-symbol is the basic building block of the Ponzano-Regge model for pure three-dimensional quantum gravity, we also discuss how to generalize the method to derive more general recursion relations on the full amplitudes.Comment: 10 pages, v2: title and introduction changed, paper re-structured; Annales Henri Poincare (2011

The First VERITAS Telescope

The first atmospheric Cherenkov telescope of VERITAS (the Very Energetic Radiation Imaging Telescope Array System) has been in operation since February 2005. We present here a technical description of the instrument and a summary of its performance. The calibration methods are described, along with the results of Monte Carlo simulations of the telescope and comparisons between real and simulated data. The analysis of TeV $\gamma$-ray observations of the Crab Nebula, including the reconstructed energy spectrum, is shown to give results consistent with earlier measurements. The telescope is operating as expected and has met or exceeded all design specifications.Comment: Accepted by Astroparticle Physic

V_us from <i>π</i> and <i>K</i> decay constants in full lattice QCD with physical <i>u</i>, <i>d</i>, <i>s</i>, and <i>c</i> quarks

We determine the decay constants of the π and K mesons on gluon field configurations from the MILC Collaboration including &lt;i&gt;u&lt;/i&gt;, &lt;i&gt;d&lt;/i&gt;, &lt;i&gt;s&lt;/i&gt;, and &lt;i&gt;c&lt;/i&gt; quarks. We use three values of the lattice spacing and &lt;i&gt;u/d&lt;/i&gt; quark masses going down to the physical value. We use the w0 parameter to fix the relative lattice spacing and fπ to fix the overall scale. This allows us to obtain a value for fK+/fπ+=1.1916(21). Comparing to the ratio of experimental leptonic decay rates gives |Vus|=0.22564(28)Br(K+)(20)EM(40)latt(5)Vud and the test of unitarity of the first row of the Cabibbo-Kobayashi-Maskawa matrix: |Vud|2+|Vus|2+|Vub|2−1=0.000 09(51)

mesenteric ischemia-reperfusion in a mouse model

To investigate the role of interleukin (IL)-10 gene therapy on the reperfusion-induced lung injury, we utilised the technique of liposomal gene delivery before the induction of intestinal ischemia. Plasmid DNA encoding human IL-10 (hIL-10) or empy vector was injected intraperitoneally 24 h before the study. Male Balb/c mice randomized into three groups: Sham operated control (n = 12), empty plasmid vector (n = 12), and hIL-10 gene therapy group (n = 12). The ischemia was generated by selective occlusion of superior mesenteric artery for 60 min. and followed by reperfusion for 30 min. Lung tissue neutrophil infiltration was determined by myeloperoxidase assay and neutrophil counts. For the determination of lung tissue microvascular permeability, Evans blue dye injection was made and the lung edema was assesed by wet/dry ratio. hIL-10 protein expression was studied by immunostaining and ELISA. We found that pre-ischemic hIL-10 overexpression attenuated dye extravasation, leukocyte sequestration and reduced pulmonary tissue injury compared to the empty vector-injected control. Our study indicates that pre-ischemic hIL-10 overexpression attenuates lung injury caused by intestinal ischemia-reperfusion. (c) 2005 Tohoku University Medical Press.C1 Pamukkale Univ, Fac Med, Dept Gen Surg, Denizli, Turkey.Pamukkale Univ, Fac Med, Dept Surg, Denizli, Turkey.Pamukkale Univ, Fac Sci Art, Dept Chem, Denizli, Turkey