Free q-Schrodinger Equation from Homogeneous Spaces of the 2-dim Euclidean Quantum Group

After a preliminary review of the definition and the general properties of the homogeneous spaces of quantum groups, the quantum hyperboloid qH and the quantum plane qP are determined as homogeneous spaces of Fq(E(2)). The canonical action of Eq(2) is used to define a natural q-analog of the free Schro"dinger equation, that is studied in the momentum and angular momentum bases. In the first case the eigenfunctions are factorized in terms of products of two q-exponentials. In the second case we determine the eigenstates of the unitary representation, which, in the qP case, are given in terms of Hahn-Exton functions. Introducing the universal T-matrix for Eq(2) we prove that the Hahn-Exton as well as Jackson q-Bessel functions are also obtained as matrix elements of T, thus giving the correct extension to quantum groups of well known methods in harmonic analysis.Comment: 19 pages, plain tex, revised version with added materia

Examples of q-regularization

An Introduction to Hopf algebras as a tool for the regularization of relavent quantities in quantum field theory is given. We deform algebraic spaces by introducing q as a regulator of a non-commutative and non-cocommutative Hopf algebra. Relevant quantities are finite provided q\neq 1 and diverge in the limit q\rightarrow 1. We discuss q-regularization on different q-deformed spaces for \lambda\phi^4 theory as example to illustrate the idea.Comment: 17 pages, LaTex, to be published in IJTP 1995.1

Spatial Resolution of Double-Sided Silicon Microstrip Detectors for the PAMELA Apparatus

The PAMELA apparatus has been assembled and it is ready to be launched in a satellite mission to study mainly the antiparticle component of cosmic rays. In this paper the performances obtained for the silicon microstrip detectors used in the magnetic spectrometer are presented. This subdetector reconstructs the curvature of a charged particle in the magnetic field produced by a permanent magnet and consequently determines momentum and charge sign, thanks to a very good accuracy in the position measurements (better than 3 um in the bending coordinate). A complete simulation of the silicon microstrip detectors has been developed in order to investigate in great detail the sensor's characteristics. Simulated events have been then compared with data gathered from minimum ionizing particle (MIP) beams during the last years in order to tune free parameters of the simulation. Finally some either widely used or original position finding algorithms, designed for such kind of detectors, have been applied to events with different incidence angles. As a result of the analysis, a method of impact point reconstruction can be chosen, depending on both the particle's incidence angle and the cluster multiplicity, so as to maximize the capability of the spectrometer in antiparticle tagging.Comment: 28 pages, 18 figures, submitted to Nuclear Instruments and Methods in Physics Research

Muography applied to nuclear waste storage sites

Legacy storage sites for nuclear waste can pose a serious environmental problem. In fact, since certain sites date from the middle of the last century when safety protocols had not been properly established and strict bookkeeping was not enforced, a situation has evolved where the content of storage silos is basically known only with a large uncertainty both on quantity and quality. At the same time maintenance work on old storage structures is becoming ever more urgent and yet this work requires exactly that information which is now lacking on the type of waste that was stored inside. Because of the difficulty in accessing the storage silos and the near impossibility of making visual inspections inside, techniques have to be developed which can determine the presence or absence of heavy elements (i.e. uranium) within the structures. Muography is a very promising technique which could allow the survey of previously inaccessible structures. We have begun an evaluation performing feasibility studies using simulations based on real case scenarios. This paper will outline the storage site scenarios and then present some of the results obtained from the Monte Carlo simulations

Differential and Twistor Geometry of the Quantum Hopf Fibration

We study a quantum version of the SU(2) Hopf fibration $S^7 \to S^4$ and its associated twistor geometry. Our quantum sphere $S^7_q$ arises as the unit sphere inside a q-deformed quaternion space $\mathbb{H}^2_q$. The resulting four-sphere $S^4_q$ is a quantum analogue of the quaternionic projective space $\mathbb{HP}^1$. The quantum fibration is endowed with compatible non-universal differential calculi. By investigating the quantum symmetries of the fibration, we obtain the geometry of the corresponding twistor space $\mathbb{CP}^3_q$ and use it to study a system of anti-self-duality equations on $S^4_q$, for which we find an `instanton' solution coming from the natural projection defining the tautological bundle over $S^4_q$.Comment: v2: 38 pages; completely rewritten. The crucial difference with respect to the first version is that in the present one the quantum four-sphere, the base space of the fibration, is NOT a quantum homogeneous space. This has important consequences and led to very drastic changes to the paper. To appear in CM

Ehrenfest times for classically chaotic systems

We describe the quantum mechanical spreading of a Gaussian wave packet by means of the semiclassical WKB approximation of Berry and Balazs. We find that the time scale $\tau$ on which this approximation breaks down in a chaotic system is larger than the Ehrenfest times considered previously. In one dimension \tau=\fr{7}{6}\lambda^{-1}\ln(A/\hbar), with $\lambda$ the Lyapunov exponent and $A$ a typical classical action.Comment: 4 page

Inomogeneous Quantum Groups as Symmetries of Phonons

The quantum deformed (1+1) Poincare' algebra is shown to be the kinematical symmetry of the harmonic chain, whose spacing is given by the deformation parameter. Phonons with their symmetries as well as multiphonon processes are derived from the quantum group structure. Inhomogeneous quantum groups are thus proposed as kinematical invariance of discrete systems.Comment: 5 pags. 0 fig

Effects and Mechanisms Activated by Treatment with Cationic, Anionic and Zwitterionic Liposomes on an In Vitro Model of Porcine Pre-Pubertal Sertoli Cells

: Liposomes have been successfully used as drug-delivery vehicles, but there are no clinical studies on improved fertility and the few reported experimental studies have been performed in animal models far from humans. The aim of this paper was to study the effects of treatment with cationic, anionic and zwitterionic liposomes on our superior mammalian model of porcine prepubertal Sertoli cells (SCs) to find a carrier of in vitro test drugs for SCs. Porcine pre-pubertal SCs cultures were incubated with different liposomes. Viability, apoptosis/necrosis status (Annexin-V/Propidium iodide assay), immunolocalisation of β-actin, vimentin, the phosphorylated form of AMP-activated protein Kinase (AMPK)α and cell ultrastructure (Transmission Electron Microscopy, TEM) were analysed. Zwitterionic liposomes did not determine changes in the cell cytoplasm. The incubation with anionic and cationic liposomes modified the distribution of actin and vimentin filaments and increased the levels of the phosphorylated form of AMPKα. The Annexin/Propidium Iodide assay suggested an increase in apoptosis. TEM analysis highlighted a cytoplasmic vacuolisation. In conclusion, these preliminary data indicated that zwitterionic liposomes were the best carrier to use in an in vitro study of SCs to understand the effects of molecules or drugs that could have a clinical application in the treatment of certain forms of male infertility

CaloCube: a novel calorimeter for high-energy cosmic rays in space

In order to extend the direct observation of high-energy cosmic rays up to the PeV region, highly performing calorimeters with large geometrical acceptance and high energy resolution are required. Within the constraint of the total mass of the apparatus, crucial for a space mission, the calorimeters must be optimized with respect to their geometrical acceptance, granularity and absorption depth. CaloCube is a homogeneous calorimeter with cubic geometry, to maximise the acceptance being sensitive to particles from every direction in space; granularity is obtained by relying on small cubic scintillating crystals as active elements. Different scintillating materials have been studied. The crystal sizes and spacing among them have been optimized with respect to the energy resolution. A prototype, based on CsI(Tl) cubic crystals, has been constructed and tested with particle beams. Some results of tests with different beams at CERN are presented.Comment: Seven pages, seven pictures. Proceedings of INSTR17 Novosibirs