18167234
Group-like objects in Poisson geometry and algebra
A group, defined as set with associative multiplication and inverse, is a natural structure describing the symmetry of a space. The concept of group generalizes to group objects internal to other categories than sets. But there are yet more general objects that can still be thought of as groups in many ways, such as quantum groups. We explain some of the generalizations of groups which arise in Poisson geometry and quantization: the germ of a topological group, Poisson Lie groups, rigid monoidal structures on symplectic realizations, groupoids, 2-groups, stacky Lie groups, and hopfish algebras.
17256168
Courant Algebroids and Strongly Homotopy Lie Algebras
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.
15512865
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.
17756587
Poisson geometry with a 3 form background
We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these "twisted" Poisson structures are conveniently described as Dirac structures in suitable Courant algebroids. The additive group of 2-forms acts on twisted Poisson structures and permits them to be seen as glued from ordinary Poisson structures defined on local patches. We conclude with remarks on deformation quantization and twisted symplectic groupoids.
121794904
A universal phase space for particles in Yang-Mills fields
Given a principal G-bundle P over M and a Hamiltonian G-space Q, one may construct the reduced symplectic manifold (T*P x Q)0. When a connection on P is chosen, this manifold becomes a bundle over T*M with fibre Q. It is shown that this bundle is precisely the phase space constructed by Sternberg for a classical particle in a Yang-Mills field.
15329636
Hopfish structure and modules over irrational rotation algebras
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.
17448418
A Study of jet production rates in the four flavor continuum and a test of QCD
We present a QCD analysis of jet production rates measured in e + e 0 annihilation into hadrons at about 10 GeV where only four avors are produced in the continuum. All previous jet studies have been performed in the ve avor continuum. In the four avor continuum QCD predictions are substantially dierent due to the dierent contributions from vacuum polarization diagrams. The measured jet rate distributions are compared to the predictions of O(2 s) QCD computed for the four avor continuum. From the ts of the theory to the data we obtain the nal value of s where the rst error is due to the experimental uncertainties and the second error includes theoretical uncertainties due to hadronization, parton virtual-ity, renormalization scale and jet resolution parameter, all added in quadra-ture. This value of s extrapolated to M Z 0 in the ve avor continuum yields s
120882870
Veritas: Status summary 2009
VERITAS is a ground-based gamma-ray observatory that uses the imaging atmospheric Cherenkov technique and operates in the very-high energy (VHE) region of the gamma-ray spectrum from 100 GeV to 50 TeV. The observatory consists of an array of four 12 m-diameter imaging atmospheric Cherenkov telescopes located in southern Arizona, USA. The four-telescope array has been fully operational since September 2007, and over the last two years, VERITAS has been operating with high reliability and sensitivity. It is currently one of the most sensitive VHE observatories. This paper summarizes the status of VERITAS as of October 2009, and describes the detection of several new VHE gamma-ray sources.
15066884
CLEO results on tau Michel parameters
We present measurements of the tau Michel Parameters made by the CLEO experiment. Three different analyses are performed: a spin-independent lepton spectrum analysis and a second spin-dependent analysis using l^± vs. π^‡π^0 events, and a third spin-dependent analysis using π^+ vs. π^− events. the results are used to derive limits on the general four-fermion couplings, the mass of the charged Higgs in the MSSM, and a right-handed W in left-right models. Many of these measurements are more precise than the PDG world averages.
124064020
Of Symmetries and Factories, Matter and Antimatter
An elusive subatomic particle called the B decays in a way that violates a fundamental symmetry of nature. Physicists hope to study this decay pattern at a "B Factory," as learning its secrets may explain why there is more matter than antimatter in the universe today.
126248406
Constraints on r($B$) and $\gamma$ in $B^\pm \to D^{(*)} 0 K^\pm$ decays by a Dalitz analysis of $D^0 \to K_{S} \pi^{-} \pi^{+}$