Conformal Field Theory Correlators from Classical Field Theory on Anti-de Sitter Space II. Vector and Spinor Fields

We use the AdS/CFT correspondence to calculate CFT correlation functions of vector and spinor fields. The connection between the AdS and boundary fields is properly treated via a Dirichlet boundary value problem.Comment: 14 pages, LaTeX2e with amsmath,amsfonts packages; v2:interactions section corrected, reference adde

Quantization on Curves

Deformation quantization on varieties with singularities offers perspectives that are not found on manifolds. Essential deformations are classified by the Harrison component of Hochschild cohomology, that vanishes on smooth manifolds and reflects information about singularities. The Harrison 2-cochains are symmetric and are interpreted in terms of abelian $*$-products. This paper begins a study of abelian quantization on plane curves over \Crm, being algebraic varieties of the form R2/I where I is a polynomial in two variables; that is, abelian deformations of the coordinate algebra C[x,y]/(I). To understand the connection between the singularities of a variety and cohomology we determine the algebraic Hochschild (co-)homology and its Barr-Gerstenhaber-Schack decomposition. Homology is the same for all plane curves C[x,y]/(I), but the cohomology depends on the local algebra of the singularity of I at the origin.Comment: 21 pages, LaTex format. To appear in Letters Mathematical Physic

Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]

Representations of the quantum superalgebra U_q[osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U_q[osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be expressed in terms of the $Q$-Hahn polynomials. We next investigate representations of the quantum supergroup OSp_q(1/2) which are not well-defined in the classical limit. Employing the universal T-matrix, the representation matrices are obtained explicitly, and found to be related to the little Q-Jacobi polynomials. Characteristically, the relation Q = -q is satisfied in all cases. Using the Clebsch-Gordan coefficients derived here, we construct new noncommutative spaces that are covariant under the coaction of the even dimensional representations of the quantum supergroup OSp_q(1/2).Comment: 16 pages, no figure

Knowledge mobilization in the context of health technology assessment: an exploratory case study

<p>Abstract</p> <p>Background</p> <p>Finding measures to enhance the dissemination and implementation of their recommendations has become part of most health technology assessment (HTA) bodies' preoccupations. The Quebec government HTA organization in Canada observed that some of its projects relied on innovative practices in knowledge production and dissemination. A research was commissioned in order to identify what characterized these practices and to establish whether they could be systematized.</p> <p>Methods</p> <p>An exploratory case study was conducted during summer and fall 2010 in the HTA agency in order to determine what made the specificity of its context, and to conceptualize an approach to knowledge production and dissemination that was adapted to the mandate and nature of this form of HTA organization. Six projects were selected. For each, the HTA report and complementary documents were analyzed, and semi-structured interviews were carried out. A narrative literature review of the most recent literature reviews of the principal knowledge into practice frameworks (2005-2010) and of articles describing such frameworks (2000-2010) was undertaken.</p> <p>Results and discussion</p> <p>Our observations highlighted an inherent difficulty as regards applying the dominant knowledge translation models to HTA and clinical guidance practices. For the latter, the whole process starts with an evaluation question asked in a problematic situation for which an actionable answer is expected. The objective is to produce the evidence necessary to respond to the decision-maker's request. The practices we have analyzed revealed an approach to knowledge production and dissemination, which was multidimensional, organic, multidirectional, dynamic, and dependent on interactions with stakeholders. Thus, HTA could be considered as a knowledge mobilization process per se.</p> <p>Conclusions</p> <p>HTA's purpose is to solve a problem by mobilizing the types of evidence required and the concerned actors, in order to support political, organizational or clinical decision-making. HTA relies on the mediation between contextual, colloquial and scientific evidence, as well as on interactions with stakeholders for recommendation making. Defining HTA as a knowledge mobilization process might contribute to consider the different orders of knowledge, the social, political and ethical dimensions, and the interactions with stakeholders, among the essential components required to respond to the preoccupations, needs and contexts of all actors concerned with the evaluation question's issues.</p

Deformation Quantization on the Closure of Minimal Coadjoint Orbits

We consider a complex simple Lie algebra $${\mathfrak{g}}$$ , with the action of its adjoint group. Among the three canonical nilpotent orbits under this action, the minimal orbit is the non zero orbit of smallest dimension. We are interested in equivariant deformation quantization: we construct $${\mathfrak{g}}$$ -invariant star-products on the minimal orbit and on its closure, a singular algebraic variety. We shall make use of Hochschild homology and cohomology, of some results about the invariants of the classical groups, and of some interesting representations of simple Lie algebras. To the minimal orbit is associated a unique, completely prime two-sided ideal of the universal enveloping algebra $${{\rm U}(\mathfrak{g})}$$ . This ideal is primitive and is called the Joseph ideal. We give explicit expressions for the generators of the Joseph ideal and compute the infinitesimal characters