15680402
Matrix Bases for Star Products: a Review
We review the matrix bases for a family of noncommutative ? products based on a Weyl map. These products include the Moyal product, as well as the Wick-Voros products and other translation invariant ones. We also review the derivation of Lie algebra type star products, with adapted matrix bases. We discuss the uses of these matrix bases for eld theory, fuzzy spaces and emergent gravity.
119414376
Phase space distributions and a duality symmetry for star products
Abstract A duality property for star products is exhibited. In view of it, known star-product schemes, like the Weyl–Wigner–Moyal formalism, the Husimi and the Glauber–Sudarshan maps are revisited. The tomographic map, which has been recently described as yet another star product scheme, is considered. It yields a noncommutative algebra of operator symbols which are positive definite probability distributions. Through the duality symmetry a new noncommutative algebra of operator symbols is found, equipped with a new star product. The kernel of the star product is established in explicit form and examples are considered.
119406176
The fuzzy disc: A review
In this talk we present a matrix approximation to the algebra of functions on the disc and define a fuzzy approximation to the Laplacian with Dirichlet boundary conditions. A basis for the NC algebra is introduced in terms of the eigenfunctions of the fuzzy Laplacian, which are seen to converge to the eigenfunctions of the ordinary Laplacian on the disc, that is, the Bessel functions.
17476222
On Reduced Time Evolution for Initially Correlated Pure States
A new method to deal with reduced dynamics of open systems by means of the Schrodinger equation is presented. It allows one to consider the reduced time evolution for correlated and uncorrelated initial conditions.
119233984
Aspects of group field theory
I review the basic ingredients of discretized gravity which motivate the introduction of Group Field Theory. Thus I describe the GFT formulation of some models and conclude with a few remarks on the emergence of noncommutative structures in such models.
115163215
Star-product in the presence of a monopole
Abstract We present a deformed ⋆-product for a particle in the presence of a magnetic monopole. The product is obtained within a self-dual quantization–dequantization scheme, with the correspondence between classical observables and operators defined with the help of a quaternionic Hilbert space, following work by Emch and Jadczyk. The resulting product is well defined for a large class of complex functions and reproduces (at first order in ℏ ) the Poisson structure of the particle in the monopole field. The product is associative only for quantized monopole charges, thus incorporating Dirac's quantization requirement.
122999968
Elemental analysis of aerosols collected at the Pierre Auger Cosmic Ray Observatory with PIXE technique complemented with SEM/EDX
Abstract The aim of this work is to characterize surface aerosols at the Pierre Auger Cosmic Ray Observatory located at Pampa Amarilla, near Malargue city, in the Andes region of Argentina, with experimental sampling techniques used for the first time in a cosmic ray observatory, adding to information provided by the existing Auger aerosol monitors. A good knowledge of the optical attenuation due to aerosols is crucial for a good reconstruction of the signals from cosmic ray showers detected by the fluorescence detectors of the Observatory. Aerosols were collected in filters, during the Southern Hemisphere winter and spring in 2008. Concentrations in PM2.5 and PM2.5–10 filters were determined by gravimetric analysis and their elemental composition by the PIXE technique, complemented with SEM/EDX. Low aerosol concentrations were measured during the sampling period. The mean total mass PM10 (=PM2.5 + PM2.5–10 fractions) value was [mean(se)] 9.8(1.0) μg/m3 [sd = 5.9 μg/m3]. The mean PM10 value during winter was 7(1.1) μg/m3 [sd = 4.5 μg/m3], about half of the 13.1(1.5) [sd = 5.7 μg/m3] measured during springtime. The PM2.5 fraction was approximately 30% of the PM10 fraction. PIXE results gave levels of S, Cl, K, Ca, Ti, Mn, Fe in the analyzed aerosol samples, showing that these elements correspond to 25% and 13% of the PM2.5 and PM2.5–10 total mass respectively. The rest of the mass was due to the elements with low Z (below 16) which cannot be detected by our X-ray setup. Comparison with SEM/EDX analysis showed that most of them were Si and Al (aluminosilicates). Our results indicate that most of the aerosols at the Auger Observatory would most likely come from the soil of the region. Due to its vast atmospheric monitoring network, the Auger Observatory is an interesting reference site for further atmospheric studies.