Complexification of Gauge Theories

For the case of a first-class constrained system with an equivariant momentum map, we study the conditions under which the double process of reducing to the constraint surface and dividing out by the group of gauge transformations $G$ is equivalent to the single process of dividing out the initial phase space by the complexification $G_C$ of $G$. For the particular case of a phase space action that is the lift of a configuration space action, conditions are found under which, in finite dimensions, the physical phase space of a gauge system with first-class constraints is diffeomorphic to a manifold imbedded in the physical configuration space of the complexified gauge system. Similar conditions are shown to hold in the infinite-dimensional example of Yang-Mills theories. As a physical application we discuss the adequateness of using holomorphic Wilson loop variables as (generalized) global coordinates on the physical phase space of Yang-Mills theory.Comment: 25pp., LaTeX, Syracuse SU-GP-93/6-2, Lisbon DF/IST 6.9

Stain Resistance of Maxillofacial Materials

The resistance of three silicone and one polyvinyl chloride maxillofacial materials to staining by tea, lipstick, and disclosing solution was measured by reflectance spectrophotometry. Changes in color caused by staining were larger than changes caused by color instability of the base elastomers or pigments under conditions of accelerated aging.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66676/2/10.1177_00220345790580050401.pd

Nonperturbative bound on high multiplicity cross sections in phi^4_3 from lattice simulation

We have looked for evidence of large cross sections at large multiplicities in weakly coupled scalar field theory in three dimensions. We use spectral function sum rules to derive bounds on total cross sections where the sum can be expresed in terms of a quantity which can be measured by Monte Carlo simulation in Euclidean space. We find that high multiplicity cross sections remain small for energies and multiplicities for which large effects had been suggested.Comment: 23 pages, revtex, seven eps figures revised version: typos corrected, some rewriting of discusion, same resul

Machine learning classification of OARSI-scored human articular cartilage using magnetic resonance imaging

SummaryObjectiveThe purpose of this study is to evaluate the ability of machine learning to discriminate between magnetic resonance images (MRI) of normal and pathological human articular cartilage obtained under standard clinical conditions.MethodAn approach to MRI classification of cartilage degradation is proposed using pattern recognition and multivariable regression in which image features from MRIs of histologically scored human articular cartilage plugs were computed using weighted neighbor distance using compound hierarchy of algorithms representing morphology (WND-CHRM). The WND-CHRM method was first applied to several clinically available MRI scan types to perform binary classification of normal and osteoarthritic osteochondral plugs based on the Osteoarthritis Research Society International (OARSI) histological system. In addition, the image features computed from WND-CHRM were used to develop a multiple linear least-squares regression model for classification and prediction of an OARSI score for each cartilage plug.ResultsThe binary classification of normal and osteoarthritic plugs yielded results of limited quality with accuracies between 36% and 70%. However, multiple linear least-squares regression successfully predicted OARSI scores and classified plugs with accuracies as high as 86%. The present results improve upon the previously-reported accuracy of classification using average MRI signal intensities and parameter values.ConclusionMRI features detected by WND-CHRM reflect cartilage degradation status as assessed by OARSI histologic grading. WND-CHRM is therefore of potential use in the clinical detection and grading of osteoarthritis

How to find the holonomy algebra of a Lorentzian manifold

Manifolds with exceptional holonomy play an important role in string theory, supergravity and M-theory. It is explained how one can find the holonomy algebra of an arbitrary Riemannian or Lorentzian manifold. Using the de~Rham and Wu decompositions, this problem is reduced to the case of locally indecomposable manifolds. In the case of locally indecomposable Riemannian manifolds, it is known that the holonomy algebra can be found from the analysis of special geometric structures on the manifold. If the holonomy algebra $\mathfrak{g}\subset\mathfrak{so}(1,n-1)$ of a locally indecomposable Lorentzian manifold $(M,g)$ of dimension $n$ is different from $\mathfrak{so}(1,n-1)$, then it is contained in the similitude algebra $\mathfrak{sim}(n-2)$. There are 4 types of such holonomy algebras. Criterion how to find the type of $\mathfrak{g}$ are given, and special geometric structures corresponding to each type are described. To each $\mathfrak{g}$ there is a canonically associated subalgebra $\mathfrak{h}\subset\mathfrak{so}(n-2)$. An algorithm how to find $\mathfrak{h}$ is provided.Comment: 15 pages; the final versio

Energy-Momentum Localization for a Space-Time Geometry Exterior to a Black Hole in the Brane World

In general relativity one of the most fundamental issues consists in defining a generally acceptable definition for the energy-momentum density. As a consequence, many coordinate-dependent definitions have been presented, whereby some of them utilize appropriate energy-momentum complexes. We investigate the energy-momentum distribution for a metric exterior to a spherically symmetric black hole in the brane world by applying the Landau-Lifshitz and Weinberg prescriptions. In both the aforesaid prescriptions, the energy thus obtained depends on the radial coordinate, the mass of the black hole and a parameter $\lambda_{0}$, while all the momenta are found to be zero. It is shown that for a special value of the parameter $\lambda_{0}$, the Schwarzschild space-time geometry is recovered. Some particular and limiting cases are also discussed.Comment: 10 pages, sections 1 and 3 slightly modified, references modified and adde

Reconstruction of Black Hole Metric Perturbations from Weyl Curvature

Perturbation theory of rotating black holes is usually described in terms of Weyl scalars $\psi_4$ and $\psi_0$, which each satisfy Teukolsky's complex master wave equation and respectively represent outgoing and ingoing radiation. On the other hand metric perturbations of a Kerr hole can be described in terms of (Hertz-like) potentials $\Psi$ in outgoing or ingoing {\it radiation gauges}. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e $\psi_4$ and $\psi_0$. We explicitly construct these relations in the nonrotating limit, preparatory to devising a corresponding approach for building up the perturbed spacetime of a rotating black hole. We discuss the application of our procedure to second order perturbation theory and to the study of radiation reaction effects for a particle orbiting a massive black hole.Comment: 6 Pages, Revtex

The imposition of Cauchy data to the Teukolsky equation I: The nonrotating case

Gravitational perturbations about a Kerr black hole in the Newman-Penrose formalism are concisely described by the Teukolsky equation. New numerical methods for studying the evolution of such perturbations require not only the construction of appropriate initial data to describe the collision of two orbiting black holes, but also to know how such new data must be imposed into the Teukolsky equation. In this paper we show how Cauchy data can be incorporated explicitly into the Teukolsky equation for non-rotating black holes. The Teukolsky function $$ and its first time derivative $\partial_t \Psi$ can be written in terms of only the 3-geometry and the extrinsic curvature in a gauge invariant way. Taking a Laplace transform of the Teukolsky equation incorporates initial data as a source term. We show that for astrophysical data the straightforward Green function method leads to divergent integrals that can be regularized like for the case of a source generated by a particle coming from infinity.Comment: 9 pages, REVTEX. Misprints corrected in formulas (2.4)-(2.7). Final version to appear in PR