The orbifold transform and its applications

We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the theory of permutation orbifolds is addressed, and the general results illustrated on the example of torus partition functions

Age and the distribution of major injury across a national trauma system

Background Trauma places a significant burden on healthcare services, and its management impacts greatly on the injured patient. The demographic of major trauma is changing as the population ages, increasingly unveiling gaps in processes of managing older patients. Key to improving patient care is the ability to characterise current patient distribution. Objectives There is no contemporary evidence available to characterise how age impacts on trauma patient distribution at a national level. Through an analysis of the Trauma Audit Research Network (TARN) database, we describe the nature of Major Trauma in England since the configuration of regional trauma networks, with focus on injury distribution, ultimate treating institution and any transfer in-between. Methods The TARN database was analysed for all patients presenting from April 2012 to the end of October 2017 in NHS England. Results About 307,307 patients were included, of which 63.8% presented directly to a non-specialist hospital (trauma unit (TU)). Fall from standing height in older patients, presenting and largely remaining in TUs, dominates the English trauma caseload. Contrary to perception, major trauma patients currently are being cared for in both specialist (major trauma centres (MTCs)) and non-specialist (TU) hospitals. Paediatric trauma accounts for <5% of trauma cases and is focussed on paediatric MTCs. Conclusions Within adult major trauma patients in England, mechanism of injury is dominated by low level falls, particularly in older people. These patients are predominately cared for in TUs. This work illustrates the reality of current care pathways for major trauma patients in England in the recently configured regional trauma networks

Note on graviton MHV amplitudes

Two new formulas which express n-graviton MHV tree amplitudes in terms of sums of squares of n-gluon amplitudes are discussed. The first formula is derived from recursion relations. The second formula, simpler because it involves fewer permutations, is obtained from the variant of the Berends, Giele, Kuijf formula given in Arxiv:0707.1035.Comment: 10 page

Microbial ecology of Thiobacillus ferrooxidans

FINAL TECHNICAL REPORT TO U.S. DEPARTMENT OF THE INTERIOR Geological Survey Washington. D.C.The contents of this report were developed in part under a grant from the Department of the Interior, U.S. Geological Survey. Grant number 14-08-0001-61313

Constructing the Tree-Level Yang-Mills S-Matrix Using Complex Factorization

A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates non-trivial (but familiar) constraints on three-particle coupling constants --- these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins >2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a tree-level S-matrix, and that complex factorization of general BCFW amplitudes follows from the factorization of four-particle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the three-particle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the S-matrix is entirely independent of field theory. We analyze the case of pure Yang-Mills, and outline a proof for gravity. For Yang-Mills, we also show that the well-known scaling behavior of BCFW-deformed amplitudes at large z is a simple consequence of factorization. For gravity, factorization in certain channels requires asymptotic behavior ~1/z^2.Comment: 35 pages, 6 figure

On Tree Amplitudes in Gauge Theory and Gravity

The BCFW recursion relations provide a powerful way to compute tree amplitudes in gauge theories and gravity, but only hold if some amplitudes vanish when two of the momenta are taken to infinity in a particular complex direction. This is a very surprising property, since individual Feynman diagrams all diverge at infinite momentum. In this paper we give a simple physical understanding of amplitudes in this limit, which corresponds to a hard particle with (complex) light-like momentum moving in a soft background, and can be conveniently studied using the background field method exploiting background light-cone gauge. An important role is played by enhanced spin symmetries at infinite momentum--a single copy of a "Lorentz" group for gauge theory and two copies for gravity--which together with Ward identities give a systematic expansion for amplitudes at large momentum. We use this to study tree amplitudes in a wide variety of theories, and in particular demonstrate that certain pure gauge and gravity amplitudes do vanish at infinity. Thus the BCFW recursion relations can be used to compute completely general gluon and graviton tree amplitudes in any number of dimensions. We briefly comment on the implications of these results for computing massive 4D amplitudes by KK reduction, as well understanding the unexpected cancelations that have recently been found in loop-level gravity amplitudes.Comment: 22 pages, 3 figure

Spinning test particles and clock effect in Schwarzschild spacetime

We study the behaviour of spinning test particles in the Schwarzschild spacetime. Using Mathisson-Papapetrou equations of motion we confine our attention to spatially circular orbits and search for observable effects which could eventually discriminate among the standard supplementary conditions namely the Corinaldesi-Papapetrou, Pirani and Tulczyjew. We find that if the world line chosen for the multipole reduction and whose unit tangent we denote as $U$ is a circular orbit then also the generalized momentum $P$ of the spinning test particle is tangent to a circular orbit even though $P$ and $U$ are not parallel four-vectors. These orbits are shown to exist because the spin induced tidal forces provide the required acceleration no matter what supplementary condition we select. Of course, in the limit of a small spin the particle's orbit is close of being a circular geodesic and the (small) deviation of the angular velocities from the geodesic values can be of an arbitrary sign, corresponding to the possible spin-up and spin-down alignment to the z-axis. When two spinning particles orbit around a gravitating source in opposite directions, they make one loop with respect to a given static observer with different arrival times. This difference is termed clock effect. We find that a nonzero gravitomagnetic clock effect appears for oppositely orbiting both spin-up or spin-down particles even in the Schwarzschild spacetime. This allows us to establish a formal analogy with the case of (spin-less) geodesics on the equatorial plane of the Kerr spacetime. This result can be verified experimentally.Comment: IOP macros, eps figures n. 2, to appear on Classical and Quantum gravity, 200

A New Measurement of the Average FUV Extinction Curve

We have measured the extinction curve in the far-ultraviolet wavelength region of (900 -- 1200 A) using spectra obtained with the Berkeley EUV/FUV spectrometer during the ORFEUS-I and the ORFEUS-II missions in 1993 and 1996. From the complete sample of early-type stars observed during these missions, we have selected pairs of stars with the same spectral type but different reddenings to measure the differential FUV extinction. We model the effects of molecular hydrogen absorption and exclude affected regions of the spectrum to determine the extinction from dust alone. We minimize errors from inaccuracies in the cataloged spectral types of the stars by making our own determinations of spectral types based on their IUE spectra. We find substantial scatter in the curves of individual star pairs and present a detailed examination of the uncertainties and their effects on each extinction curve. We find that, given the potentially large uncertainties inherent in using the pair method at FUV wavelengths, a careful analysis of measurement uncertainties is critical to assessing the true dust extinction. We present a new measurement of the average far-ultraviolet extinction curve to the Lyman limit; our new measurement is consistent with an extrapolation of the standard extinction curve of Savage & Mathis (1979).Comment: 13 pages text, 7 figures 4 tables. Sent as gzipped tar, with ms.tex and 7 figure

Second-order gravitational self-force

We derive an expression for the second-order gravitational self-force that acts on a self-gravitating compact-object moving in a curved background spacetime. First we develop a new method of derivation and apply it to the derivation of the first-order gravitational self-force. Here we find that our result conforms with the previously derived expression. Next we generalize our method and derive a new expression for the second-order gravitational self-force. This study also has a practical motivation: The data analysis for the planned gravitational wave detector LISA requires construction of waveforms templates for the expected gravitational waves. Calculation of the two leading orders of the gravitational self-force will enable one to construct highly accurate waveform templates, which are needed for the data analysis of gravitational-waves that are emitted from extreme mass-ratio binaries.Comment: 35 page

Dynamics of test bodies with spin in de Sitter spacetime

We study the motion of spinning test bodies in the de Sitter spacetime of constant positive curvature. With the help of the 10 Killing vectors, we derive the 4-momentum and the tensor of spin explicitly in terms of the spacetime coordinates. However, in order to find the actual trajectories, one needs to impose the so-called supplementary condition. We discuss the dynamics of spinning test bodies for the cases of the Frenkel and Tulczyjew conditions.Comment: 11 pages, RevTex forma