Dilatation operator and Cayley graphs

We use the algebraic definition of the Dilatation operator provided by Minahan, Zarembo, Beisert, Kristijansen, Staudacher, proper for single trace products of scalar fields, at leading order in the large-N 't Hooft limit to develop a new approach to the evaluation of the spectrum of the Dilatation operator. We discover a vast number of exact sequences of eigenstates.Comment: 30 pages and 3 eps figures, v2: few typos correcte

Legal medical consideration of alzheimer’s disease patients’ dysgraphia and cognitive dysfunction: a 6 month follow up

Background: The purpose of this study was to investigate the ability of Alzheimer’s disease (AD) patients to express intentions and desires, and their decision-making capacity. This study examines the findings from a 6-month follow-up of our previous results in which 30 patients participated. Materials and methods: The patient’s cognition was examined by conducting the tests of 14 questions and letter-writing ability over a period of 19 days, and it was repeated after 6 months. The difference between these two cognitive measures (PQ1 before–PQ2 before), tested previously and later the writing test, was designated DΔ before. The test was repeated after 6 months, and PQ1 after–PQ2 after was designated DΔ after. Results: Several markedly strong relationships between dysgraphia and other measures of cognitive performance in AD patients were observed. The most aged patients (over 86 years), despite less frequency, maintain the cognitive capacity manifested in the graphic expressions. A document, written by an AD patient presents an honest expression of the patient’s intention if that document is legible, clear, and comprehensive. Conclusion: The identification of impairment/deficits in writing and cognition during different phases of AD may facilitate the understanding of disease progression and identify the occasions during which the patient may be considered sufficiently lucid to make decisions. Keywords: cognition, intentions, unfit to plead, consen

Developments and new applications of numerical stochastic perturbation theory

A review of new developments in numerical stochastic perturbation theory (NSPT) is presented. In particular, the status of the extension of the method to gauge fixed lattice QCD is reviewed and a first application to compact (scalar) QED is presented. Lacking still a general proof of the convergence of the underlying stochastic processes, a self-consistent method for testing the results is discussed.Comment: 3 pages, 1 figure. Poster presented at the Lattice97 conference, Edinburgh, U

Time evolution for quantum systems at finite temperature

This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation is non-perturbative and fully quantized. Various numerical methods used to compute the needed path integrals in complex time were tested and their effectiveness was compared. For checking the formalism we used the harmonic oscillator where the numerical results could be compared with exact solutions. Interesting results were also obtained for a system that presents tunneling. A ring of coupled oscillators was treated in order to try to check selfconsistency in the thermodynamic limit. The short time distribution seems to propagate causally in the relativistic case. Our formalism can be extended easily to field theories where it remains to be seen if relevant models will be computable.Comment: uuencoded, 14 pp in Latex, 8 ps Fig

New issues for Numerical Stochastic Perturbation Theory

First attempts in the application of Numerical Stochastic Perturbation Theory (NSPT) to the problem of pushing one loop further the computation of SU(3) (SU(2)) pertubative beta function (in different schemes) are reviewed and the relevance of such a computation is discussed. Other issues include the proposal of a different strategy for gauge-fixed NSPT computations in lattice QCD.Comment: 3 pages, Latex, LATTICE98(algorithms

Vector coherent state representations, induced representations, and geometric quantization: I. Scalar coherent state representations

Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced unitary representations corresponding to prequantization; and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polarization. These representations establish an intimate relation between coherent state theory and geometric quantization in the context of induced representations.Comment: 29 pages, part 1 of two papers, published versio

In Situ Manipulation of Vertically Migrating Gelatinous Zooplankton Using Nighttime Blue-Water Scuba in the South-Central Adriatic Sea

Technological advance in undersea exploration (e.g. tethered cameras, remotely operated vehicles [ROVs], Autonomous Underwater Vehicles [AUVsG, and manned submersibles)have opened new windows into diversityand distribution of fragile gelatinous organisms in the vast mesopelagic realm(300 m-1000 m deep). While exstraordinary in expanding our view of its richness, mesopelagic exploration remains largely a look but don\u27t touch environment and this limits of our ability to understand these animals through physical manipulation relevant to the finer scales of the individual organism. We have been conducting a series of in situ observations and manipulations using blue-water SCUBA during the night at a 1, 200 m station centraly located in the southern Adriatic Sea. We report here on a suite of vertically migrating gelatinous animals, including the narcomedusa Solmissus albescens and the physonect siphonophores Forskalia formosa and Agalma elegans, whose ranges extend to the mesopelagic realm during the day, but reach SCUBA diving depths during the night. Our in situ approach combined with proximity to shore exploits the natural vertical migratory behavior of some mesopelagic species, and we therefore add to the widening spectrum of methods needed to evaluate these ecologically important yet difficult to study organisms

On the supersymmetric vacua of the Veneziano-Wosiek model

We study the supersymmetric vacua of the Veneziano-Wosiek model in sectors with fermion number F=2, 4 at finite 't Hooft coupling lambda. We prove that for F=2 there are two zero energy vacua for lambda > lambda_c = 1 and none otherwise. We give the analytical expressions of both vacua. One of them was previously known, the second one is obtained by solving the cohomology of the supersymmetric charges. At F=4 we compute the would-be supersymmetric vacua at high order in the the strong coupling expansion and provide strong support to the conclusion that lambda = 1 is a critical point in this sector too. It separates a strong coupling phase with two symmetric vacua from a weak coupling phase with positive spectrum.Comment: 17 pages, 2 eps figure

Decomposition of Hilbert space in sets of coherent states

Within the generalized definition of coherent states as group orbits we study the orbit spaces and the orbit manifolds in the projective spaces constructed from linear representations. Invariant functions are suggested for arbitrary groups. The group SU(2) is studied in particular and the orbit spaces of its j=1/2 and j=1 representations completely determined. The orbits of SU(2) in CP^N can be either 2 or 3 dimensional, the first of them being either isomorphic to S^2 or to RP^2 and the latter being isomorphic to quotient spaces of RP^3. We end with a look from the same perspective to the quantum mechanical space of states in particle mechanics.Comment: revtex, 13 pages, 12 figure

Supercoherent States, Super K\"ahler Geometry and Geometric Quantization

Generalized coherent states provide a means of connecting square integrable representations of a semi-simple Lie group with the symplectic geometry of some of its homogeneous spaces. In the first part of the present work this point of view is extended to the supersymmetric context, through the study of the OSp(2/2) coherent states. These are explicitly constructed starting from the known abstract typical and atypical representations of osp(2/2). Their underlying geometries turn out to be those of supersymplectic OSp(2/2) homogeneous spaces. Moment maps identifying the latter with coadjoint orbits of OSp(2/2) are exhibited via Berezin's symbols. When considered within Rothstein's general paradigm, these results lead to a natural general definition of a super K\"ahler supermanifold, the supergeometry of which is determined in terms of the usual geometry of holomorphic Hermitian vector bundles over K\"ahler manifolds. In particular, the supergeometry of the above orbits is interpreted in terms of the geometry of Einstein-Hermitian vector bundles. In the second part, an extension of the full geometric quantization procedure is applied to the same coadjoint orbits. Thanks to the super K\"ahler character of the latter, this procedure leads to explicit super unitary irreducible representations of OSp(2/2) in super Hilbert spaces of $L^2$ superholomorphic sections of prequantum bundles of the Kostant type. This work lays the foundations of a program aimed at classifying Lie supergroups' coadjoint orbits and their associated irreducible representations, ultimately leading to harmonic superanalysis. For this purpose a set of consistent conventions is exhibited.Comment: 53 pages, AMS-LaTeX (or LaTeX+AMSfonts