Heun Functions and the energy spectrum of a charged particle on a sphere under magnetic field and Coulomb force

We study the competitive action of magnetic field, Coulomb repulsion and space curvature on the motion of a charged particle. The three types of interaction are characterized by three basic lengths: l_{B} the magnetic length, l_{0} the Bohr radius and R the radius of the sphere. The energy spectrum of the particle is found by solving a Schr\"odinger equation of the Heun type, using the technique of continued fractions. It displays a rich set of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take definite values.Comment: 12 pages, 5 figures, accepted to JOPA, november 200

New solutions of Heun general equation

We show that in four particular cases the derivative of the solution of Heun general equation can be expressed in terms of a solution to another Heun equation. Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun equation for the mentioned cases. Each of the hypergeometric functions involved has correct singular behavior at only one of the singular points of the equation; the sum, however, has correct behavior

Structure of Higher Spin Gauge Interactions

In a previous paper, higher spin gauge field theory was formulated in an abstract way, essentially only keeping enough machinery to discuss "gauge invariance" of an "action". The approach could be thought of as providing an interface (or syntax) towards an implementation (or semantics) yet to be constructed. The structure then revealed turns out to be that of a strongly homotopy Lie algebra. In the present paper, the framework will be connected to more conventional field theoretic concepts. The Fock complex vertex operator implementation of the interactions in the BRST-BV formulation of the theory will be elaborated. The relation between the vertex order expansion and homological perturbation theory will be clarified. A formal non-obstruction argument is reviewed. The syntactically derived sh-Lie algebra structure is semantically mapped to the Fock complex implementation and it is shown that the recursive equations governing the higher order vertices are reproduced. Global symmetries and subsidiary conditions are discussed and as a result the tracelessness constraints are discarded. Thus all equations needed to compute the vertices to any order are collected. The framework is general enough to encompass all possible interaction terms. Finally, the abstract framework itself will be strengthened by showing that it can be naturally phrased in terms of the theory of categories.Comment: A few changes and additions made in the Introduction. Three references added. Typos corrected. Text agrees with published version in J. Math. Phys. except for minor journal specific proof-reading changes. 61 page

A Pedagogical Review of Electroweak Symmetry Breaking Scenarios

We review different avenues of electroweak symmetry breaking explored over the years. This constitutes a timely exercise as the world's largest and the highest energy particle accelerator, namely, the Large Hadron Collider (LHC) at CERN near Geneva, has started running whose primary mission is to find the Higgs or some phenomena that mimic the effects of the Higgs, i.e. to unravel the mysteries of electroweak phase transition. In the beginning, we discuss the Standard Model Higgs mechanism. After that we review the Higgs sector of the Minimal Supersymmetric Standard Model. Then we take up three relatively recent ideas: Little Higgs, Gauge-Higgs Unification, and Higgsless scenarios. For the latter three cases, we first present the basic ideas and restrict our illustration to some instructive toy models to provide an intuitive feel of the underlying dynamics, and then discuss, for each of the three cases, how more realistic scenarios are constructed and how to decipher their experimental signatures. Wherever possible, we provide enough pedagogical details, which the beginners might find useful.Comment: 45 pages, Review based on a series of lectures; v2: 63 pages, substantially expanded, references added, to appear in `Reports on Progress in Physics

Top quark physics in hadron collisions

The top quark is the heaviest elementary particle observed to date. Its large mass makes the top quark an ideal laboratory to test predictions of perturbation theory concerning heavy quark production at hadron colliders. The top quark is also a powerful probe for new phenomena beyond the Standard Model of particle physics. In addition, the top quark mass is a crucial parameter for scrutinizing the Standard Model in electroweak precision tests and for predicting the mass of the yet unobserved Higgs boson. Ten years after the discovery of the top quark at the Fermilab Tevatron top quark physics has entered an era where detailed measurements of top quark properties are undertaken. In this review article an introduction to the phenomenology of top quark production in hadron collisions is given, the lessons learned in Tevatron Run I are summarized, and first Run II results are discussed. A brief outlook to the possibilities of top quark research a the Large Hadron Collider, currently under construction at CERN, is included.Comment: 84 pages, 32 figures, accepted for publication by Reports on Progress in Physic

Inclusive education for deaf students: literacy practices and South African sign language

This is an Accepted Manuscript of an article published by Taylor & Francis in Southern African Linguistics and Applied Language Studies on 16 July 2012, available online: http://www.tandfonline.com/10.2989/16073614.2012.693707.This article considers the feasibility of inclusive education for Deaf students in a mainstream Further Education and Training (FET) classroom through the use of a South African Sign Language interpreter. It revisits the centrality of language in Deaf students' education and reports on progressive policy changes in the areas of language, education and disability in South Africa. The article surveys classroom discourse and literacy practices in a mainstream FET classroom, focusing particularly on students' acquisition of text literacy skills in Business English. Drawing on theoretical frameworks from the New Literacy Studies, Critical Discourse Analysis and the Social Model of Disability, the article argues that there is definitely potential for establishing inclusive education for Deaf students in a mainstream classroom. It however highlights that there are many difficulties and challenges around providing fully inclusive education for Deaf students. It was found that the signed interpretations in this classroom frequently represent an impoverished form of language while some types of pedagogic practice impede the interpreter's signing. The article concludes that interpreters and teachers need to be trained in forms of language and pedagogy that would benefit all students in class, including Deaf students