344 research outputs found

    Calculating Casimir Energies in Renormalizable Quantum Field Theory

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    Quantum vacuum energy has been known to have observable consequences since 1948 when Casimir calculated the force of attraction between parallel uncharged plates, a phenomenon confirmed experimentally with ever increasing precision. Casimir himself suggested that a similar attractive self-stress existed for a conducting spherical shell, but Boyer obtained a repulsive stress. Other geometries and higher dimensions have been considered over the years. Local effects, and divergences associated with surfaces and edges have been studied by several authors. Quite recently, Graham et al. have re-examined such calculations, using conventional techniques of perturbative quantum field theory to remove divergences, and have suggested that previous self-stress results may be suspect. Here we show that the examples considered in their work are misleading; in particular, it is well-known that in two dimensions a circular boundary has a divergence in the Casimir energy for massless fields, while for general dimension DD not equal to an even integer the corresponding Casimir energy arising from massless fields interior and exterior to a hyperspherical shell is finite. It has also long been recognized that the Casimir energy for massive fields is divergent for D1D\ne1. These conclusions are reinforced by a calculation of the relevant leading Feynman diagram in DD and three dimensions. There is therefore no doubt of the validity of the conventional finite Casimir calculations.Comment: 25 pages, REVTeX4, 1 ps figure. Revision includes new subsection 4B and Appendix, and other minor correction

    A Measurement of Time-Averaged Aerosol Optical Depth using Air-Showers Observed in Stereo by HiRes

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    Air fluorescence measurements of cosmic ray energy must be corrected for attenuation of the atmosphere. In this paper we show that the air-showers themselves can yield a measurement of the aerosol attenuation in terms of optical depth, time-averaged over extended periods. Although the technique lacks statistical power to make the critical hourly measurements that only specialized active instruments can achieve, we note the technique does not depend on absolute calibration of the detector hardware, and requires no additional equipment beyond the fluorescence detectors that observe the air showers. This paper describes the technique, and presents results based on analysis of 1258 air-showers observed in stereo by the High Resolution Fly's Eye over a four year span.Comment: 7 pages, 3 figures, accepted for publication by Astroparticle Physics Journa

    Geometries with Killing Spinors and Supersymmetric AdS Solutions

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    The seven and nine dimensional geometries associated with certain classes of supersymmetric AdS3AdS_3 and AdS2AdS_2 solutions of type IIB and D=11 supergravity, respectively, have many similarities with Sasaki-Einstein geometry. We further elucidate their properties and also generalise them to higher odd dimensions by introducing a new class of complex geometries in 2n+22n+2 dimensions, specified by a Riemannian metric, a scalar field and a closed three-form, which admit a particular kind of Killing spinor. In particular, for n3n\ge 3, we show that when the geometry in 2n+22n+2 dimensions is a cone we obtain a class of geometries in 2n+12n+1 dimensions, specified by a Riemannian metric, a scalar field and a closed two-form, which includes the seven and nine-dimensional geometries mentioned above when n=3,4n=3,4, respectively. We also consider various ansatz for the geometries and construct infinite classes of explicit examples for all nn.Comment: 28 page

    Diagnostic evaluation of infants with recurrent or persistent wheezing

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    The Pediatric Assembly of the American Thoracic Society assembled an interdisciplinary panel to develop clinical practice guidelines for the evaluation of infants with recurrent or persistent wheezing. This summary of the guideline is intended for practicing clinicians

    Molecular dynamics simulation of the order-disorder phase transition in solid NaNO2_2

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    We present molecular dynamics simulations of solid NaNO2_2 using pair potentials with the rigid-ion model. The crystal potential surface is calculated by using an \emph{a priori} method which integrates the \emph{ab initio} calculations with the Gordon-Kim electron gas theory. This approach is carefully examined by using different population analysis methods and comparing the intermolecular interactions resulting from this approach with those from the \emph{ab initio} Hartree-Fock calculations. Our numerics shows that the ferroelectric-paraelectric phase transition in solid NaNO2_2 is triggered by rotation of the nitrite ions around the crystallographical c axis, in agreement with recent X-ray experiments [Gohda \textit{et al.}, Phys. Rev. B \textbf{63}, 14101 (2000)]. The crystal-field effects on the nitrite ion are also addressed. Remarkable internal charge-transfer effect is found.Comment: RevTeX 4.0, 11 figure

    On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

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    We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.Comment: 28 page

    Pseudo-hyperkahler Geometry and Generalized Kahler Geometry

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    We discuss the conditions for additional supersymmetry and twisted supersymmetry in N = (2, 2) supersymmetric non-linear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that have an algebra that closes off-shell. We find that additional linear supersymmetry has no interesting solution, whereas additional linear twisted supersymmetry has solutions with interesting geometrical properties. We solve the conditions for invariance of the action and show that these solutions correspond to a bi-hermitian metric of signature (2, 2) and a pseudo-hyperkaehler geometry of the target space.Comment: Letters in Mathematical Physics : electronically published versio

    Observation of the Ankle and Evidence for a High-Energy Break in the Cosmic Ray Spectrum

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    We have measured the cosmic ray spectrum at energies above 101710^{17} eV using the two air fluorescence detectors of the High Resolution Fly's Eye experiment operating in monocular mode. We describe the detector, PMT and atmospheric calibrations, and the analysis techniques for the two detectors. We fit the spectrum to models describing galactic and extragalactic sources. Our measured spectrum gives an observation of a feature known as the ``ankle'' near 3×10183\times 10^{18} eV, and strong evidence for a suppression near 6×10196\times 10^{19} eV.Comment: 14 pages, 9 figures. To appear in Physics Letters B. Accepted versio

    Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity

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    From the beginning of the subject, calculations of quantum vacuum energies or Casimir energies have been plagued with two types of divergences: The total energy, which may be thought of as some sort of regularization of the zero-point energy, 12ω\sum\frac12\hbar\omega, seems manifestly divergent. And local energy densities, obtained from the vacuum expectation value of the energy-momentum tensor, T00\langle T_{00}\rangle, typically diverge near boundaries. The energy of interaction between distinct rigid bodies of whatever type is finite, corresponding to observable forces and torques between the bodies, which can be unambiguously calculated. The self-energy of a body is less well-defined, and suffers divergences which may or may not be removable. Some examples where a unique total self-stress may be evaluated include the perfectly conducting spherical shell first considered by Boyer, a perfectly conducting cylindrical shell, and dilute dielectric balls and cylinders. In these cases the finite part is unique, yet there are divergent contributions which may be subsumed in some sort of renormalization of physical parameters. The divergences that occur in the local energy-momentum tensor near surfaces are distinct from the divergences in the total energy, which are often associated with energy located exactly on the surfaces. However, the local energy-momentum tensor couples to gravity, so what is the significance of infinite quantities here? For the classic situation of parallel plates there are indications that the divergences in the local energy density are consistent with divergences in Einstein's equations; correspondingly, it has been shown that divergences in the total Casimir energy serve to precisely renormalize the masses of the plates, in accordance with the equivalence principle.Comment: 53 pages, 1 figure, invited review paper to Lecture Notes in Physics volume in Casimir physics edited by Diego Dalvit, Peter Milonni, David Roberts, and Felipe da Ros
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