Inequivalent Quantizations of Gauge Theories

It is known that the quantization of a system defined on a topologically non-trivial configuration space is ambiguous in that many inequivalent quantum systems are possible. This is the case for multiply connected spaces as well as for coset spaces. Recently, a new framework for these inequivalent quantizations approach has been proposed by McMullan and Tsutsui, which is based on a generalized Dirac approach. We employ this framework for the quantization of the Yang-Mills theory in the simplest fashion. The resulting inequivalent quantum sectors are labelled by quantized non-dynamical topological charges.Comment: 24 pages, LaTeX, to be publ. in Int.J.Mod.Phys.

Sphingosine-1-phosphate receptor 2 restrains egress of γδ T cells from the skin.

Maintenance of a population of IL-17-committed γδ T cells in the dermis is important in promoting tissue immunity. However, the signals facilitating γδ T cell retention within the dermis remain poorly understood. Here, we find that sphingosine-1-phosphate receptor 2 (S1PR2) acts in a cell-intrinsic manner to oppose γδ T cell migration from the dermis to the skin draining lymph node (dLN). Migration of dermal γδ T cells to the dLN under steady-state conditions occurs in an S1PR1-dependent manner. S1PR1 and CD69 are reciprocally expressed on dermal γδ T cells, with loss of CD69 associated with increased S1PR1 expression and enhanced migration to the dLN. γδ T cells lacking both S1PR2 and CD69 are impaired in their maintenance within the dermis. These findings provide a mechanism for how IL-17+ γδ T cells establish residence within the dermis and identify a role for S1PR2 in restraining the egress of tissue-resident lymphocytes

De-aliasing Undersampled Volume Images for Visualization

We present and illustrate a new technique, Image Correlation Supersampling (ICS), for resampling volume data that are undersampled in one dimension. The resulting data satisfies the sampling theorem, and, therefore, many visualization algorithms that assume the theorem is satisfied can be applied to the data. Without the supersampling the visualization algorithms create artifacts due to aliasing. The assumptions made in developing the algorithm are often satisfied by data that is undersampled temporally. Through this supersampling we can completely characterize phenomena with measurements at a coarser temporal sampling rate than would otherwise be necessary. This can save acquisition time and storage space, permit the study of faster phenomena, and allow their study without introducing aliasing artifacts. The resampling technique relies on a priori knowledge of the measured phenomenon, and applies, in particular, to scalar concentration measurements of fluid flow. Because of the characteristics of fluid flow, an image deformation that takes each slice image to the next can be used to calculate intermediate slice images at arbitrarily fine spacing. We determine the deformation with an automatic, multi-resolution algorithm

Path Integrals on Riemannian Manifolds with Symmetry and Induced Gauge Structure

We formulate path integrals on any Riemannian manifold which admits the action of a compact Lie group by isometric transformations. We consider a path integral on a Riemannian manifold M on which a Lie group G acts isometrically. Then we show that the path integral on M is reduced to a family of path integrals on a quotient space Q=M/G and that the reduced path integrals are completely classified by irreducible unitary representations of G. It is not necessary to assume that the action of G on M is either free or transitive. Hence our formulation is applicable to a wide class of manifolds, which includes inhomogeneous spaces, and it covers all the inequivalent quantizations. To describe the path integral on inhomogeneous space, stratification geometry, which is a generalization of the concept of principal fiber bundle, is necessarily introduced. Using it we show that the path integral is expressed as a product of three factors; the rotational energy amplitude, the vibrational energy amplitude, and the holonomy factor. When a singular point arises in $Q$, we determine the boundary condition of the path integral kernel for a path which runs through the singularity.Comment: 20 pages, no figur

Oxidative Addition of Aryl Electrophiles to a Prototypical Nickel(0) Complex: Mechanism and Structure/Reactivity Relationships

Detailed kinetic studies of the reaction of a model Ni-0 complex with a range of aryl electrophiles have been conducted. The reactions proceed via a fast ligand exchange pre-equilibrium, followed by oxidative addition to produce either [(NiX)-X-I(dppf)] (and biaryl) or [Ni-II(Ar)X(dppf)]; the ortho substituent of the aryl halide determines selectivity between these possibilities. A reactivity scale is presented in which a range of substrates is quantitatively ranked in order of the rate at which they undergo oxidative addition. The rate of oxidative addition is loosely correlated to conversion in prototypical cross-coupling reactions. Substrates that lead to Ni-I products in kinetic experiments conditions. produce more homocoupling products under catalytic conditions

An Analysis of the Representations of the Mapping Class Group of a Multi-Geon Three-Manifold

It is well known that the inequivalent unitary irreducible representations (UIR's) of the mapping class group $G$ of a 3-manifold give rise to ``theta sectors'' in theories of quantum gravity with fixed spatial topology. In this paper, we study several families of UIR's of $G$ and attempt to understand the physical implications of the resulting quantum sectors. The mapping class group of a three-manifold which is the connected sum of $\R^3$ with a finite number of identical irreducible primes is a semi-direct product group. Following Mackey's theory of induced representations, we provide an analysis of the structure of the general finite dimensional UIR of such a group. In the picture of quantized primes as particles (topological geons), this general group-theoretic analysis enables one to draw several interesting qualitative conclusions about the geons' behavior in different quantum sectors, without requiring an explicit knowledge of the UIR's corresponding to the individual primes.Comment: 52 pages, harvmac, 2 postscript figures, epsf required. Added an appendix proving the semi-direct product structure of the MCG, corrected an error in the characterization of the slide subgroup, reworded extensively. All our analysis and conclusions remain as befor

On a Modification of the Boundary State Formalism in Off-shell String Theory

We examine the application of boundary states in computing amplitudes in off-shell open string theory. We find a straightforward generalization of boundary state which produces the correct matrix elements with on-shell closed string states.Comment: Latex, 10 pages, refs added, minor typos correcte

The Boundary State Formalism and Conformal Invariance in Off-shell String Theory

We present a generalization of the boundary state formalism for the bosonic string that allows us to calculate the overlap of the boundary state with arbitrary closed string states. We show that this generalization exactly reproduces world-sheet sigma model calculations, thus giving the correct overlap with both on- and off-shell string states, and that this new boundary state automatically satisfies the requirement for integrated vertex operators in the case of non-conformally invariant boundary interactions.Comment: 19 pages, 0 figure