67 research outputs found

    A Note on Lie-Lorentz Derivatives

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    The definition of ``Lie derivative'' of spinors with respect to Killing vectors is extended to all kinds of Lorentz tensors. This Lie-Lorentz derivative appears naturally in the commutator of two supersymmetry transformations generated by Killing spinors and vanishes for Vielbeins. It can be identified as the generator of the action of isometries on supergravity fields and its use for the calculation of supersymmetry algebras is revised and extended.Comment: Latex2e, 9 pages, AMS font

    The Sun's position in the sky

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    We express the position of the Sun in the sky as a function of time and the observer's geographic coordinates. Our method is based on applying rotation matrices to vectors describing points on the celestial sphere. We also derive direct expressions, as functions of date of the year and geographic latitude, for the duration of daylight, the maximum and minimum altitudes of the Sun, and the cardinal directions to sunrise and sunset. We discuss how to account for the eccentricity of the earth's orbit, the precessions of the equinoxes and the perihelion, the size of the solar disk, and atmospheric refraction. We illustrate these results by computing the dates of "Manhattanhenge" (when sunset aligns with the east-west streets on the main traffic grid for Manhattan, in New York City), by plotting the altitude of the Sun over representative cities as a function of time, and by showing plots ("analemmas") for the position of the Sun in the sky at a given hour of the day.Comment: 19 pages, 16 figures. v3: Replaced to match published version and to re-package Mathematica notebook as an ancillary fil

    Maxwell's theory on a post-Riemannian spacetime and the equivalence principle

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    The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if torsion and/or nonmetricity fields are allowed for in spacetime. Starting from the conservation laws of electric charge and magnetic flux, we recognize that the Maxwell equations themselves remain the same, but the constitutive law must depend on the metric and, additionally, may depend on quantities related to torsion and/or nonmetricity. We illustrate our results by putting an electric charge on top of a spherically symmetric exact solution of the metric-affine gauge theory of gravity (comprising torsion and nonmetricity). All this is compared to the recent results of Vandyck.Comment: 9 pages, REVTeX, no figures; minor changes, version to be published in Class. Quantum Gra

    Coherent methods in the X-ray sciences

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    X-ray sources are developing rapidly and their coherent output is growing extremely rapidly. The increased coherent flux from modern X-ray sources is being matched with an associated rapid development in experimental methods. This article reviews the literature describing the ideas that utilise the increased brilliance from modern X-ray sources. It explores how ideas in coherent X-ray science are leading to developments in other areas, and vice versa. The article describes measurements of coherence properties and uses this discussion as a base from which to describe partially-coherent diffraction and X-ray phase contrast imaging, with its applications in materials science, engineering and medicine. Coherent diffraction imaging methods are reviewed along with associated experiments in materials science. Proposals for experiments to be performed with the new X-ray free-electron-lasers are briefly discussed. The literature on X-ray photon correlation spectroscopy is described and the features it has in common with other coherent X-ray methods are identified. Many of the ideas used in the coherent X-ray literature have their origins in the optical and electron communities and these connections are explored. A review of the areas in which ideas from coherent X-ray methods are contributing to methods for the neutron, electron and optical communities is presented.Comment: A review articel accepted by Advances in Physics. 158 pages, 29 figures, 3 table

    Butterflies fall in Flanders fields

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