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

On the 3-particle scattering continuum in quasi one dimensional integer spin Heisenberg magnets

We analyse the three-particle scattering continuum in quasi one dimensional integer spin Heisenberg antiferromagnets within a low-energy effective field theory framework. We exactly determine the zero temperature dynamical structure factor in the O(3) nonlinear sigma model and in Tsvelik's Majorana fermion theory. We study the effects of interchain coupling in a Random Phase Approximation. We discuss the application of our results to recent neutron-scattering experiments on the Haldane-gap material ${\rm CsNiCl_3}$.Comment: 8 pages of revtex, 5 figures, small changes, to appear in PR

Total and differential cross sections of η-production in proton–deuteron fusion for excess energies between Qη = 13 MeV and Qη = 81 MeV

New data on both total and differential cross sections of the production of η mesons in proton–deuteron fusion to He3η in the excess energy region 13.6MeV≤Qη≤80.9MeV are presented. These data have been obtained with the WASA-at-COSY detector setup located at the Forschungszentrum Jülich, using a proton beam at 15 different beam momenta between pp=1.60GeV/c and pp=1.74GeV/c. While significant structure of the total cross section is observed in the energy region 20MeV≲Qη≲60MeV, a previously reported sharp variation around Qη≈50MeV cannot be confirmed. Angular distributions show the typical forward-peaking that was noted earlier. For the first time, it is possible to study the development of these angular distributions with rising excess energy over a wide interval

EFFICIENCY OF EVALUATION OF THE TECHNICAL STATE OF THE RADIO-LOCATION SYSTEM OF MILITARY POWERS OF UKRAINE

Пропонується методика визначення ефективності оцінювання технічного стану радіолокаційної системи Збройних Сил України з використанням автоматизованої системи контролю, елементи якої розгортаються у радіотехнічних військах Повітряних Сил. Обговорюються умови та методи контролю справності та технічних характеристик радіолокаційних засобів як нового, так і старого парку. Обираються та описуються показники для визначення ефективності оцінювання технічного стану радіолокаційної системи:достовірність оцінювання, своєчасність заходів контролю, повнота охоплення контролем радіоелектронної техніки за допустимий на його проведення час. Визначаються математичний апарат на основі методів статистичного контролю якості і теорії надійності та порядок розрахунку запропонованих показників.Предлагается методика определения эффективности оценивания технического состояния радиолокационной системы Вооруженных Сил Украины с использованием автоматизированной системы контроля, элементы которой разворачиваются в радиотехнических войсках Воздушных Сил. Обсуждаются условия и методы контроля исправности и технических характеристик радиолокационных средств как нового, так и старого парка. Выбираются и описываются показатели для определения эффективности оценивания технического состояния радиолокационной системи: достовірність оценивания, своевременность мероприятий контроля, полнота охвата контролем радиоэлектронной техники за допустимое на его проведение время. Определяется математический аппарат на основе методов статистического контроля качества и теории надежности и порядок расчета предложенных показателей.The method of definition of efficiency of evaluation of the technical state of the radio-location system of Military Powers of Ukraine is offered with the use of the automated checking system the elements of which are opened out in the radio engineerings troops of Aircrafts. Terms and methods of control of good condition and technical descriptions of radio-location facilities of both new and old park come into a question. Get out and described indexes for definition of efficiency of evaluation of the technical state of radio-location sistems: evaluations, timeliness of control measures, plenitude of scope control of radio electronic technique for possible on its leadthrough time. A mathematical vehicle on the basis of methods of statistical control of quality and theory of reliability and order of calculation of the offered indexes is determined