Background field technique and renormalization in lattice gauge theory

Lattice gauge theory with a background gauge field is shown to be renormalizable to all orders of perturbation theory. No additional counterterms are required besides those already needed in the absence of the background field. The argument closely follows the treatment given earlier for the case of dimensional regularization by Kluberg-Stern and Zuber. It is based on the BRS, background gauge and shift symmetries of the lattice functional integral.Comment: 26 pages, uuencoded compressed postscript fil

Fedosov supermanifolds: II. Normal coordinates

The study of recently introduced Fedosov supermanifolds is continued. Using normal coordinates, properties of even and odd symplectic supermanifolds endowed with a symmetric connection respecting given sympletic structure are studied.Comment: 12 pages, Late

Loop calculations in quantum-mechanical non-linear sigma models

By carefully analyzing the relations between operator methods and the discretized and continuum path integral formulations of quantum-mechanical systems, we have found the correct Feynman rules for one-dimensional path integrals in curved spacetime. Although the prescription how to deal with the products of distributions that appear in the computation of Feynman diagrams in configuration space is surprising, this prescription follows unambiguously from the discretized path integral. We check our results by an explicit two-loop calculation.Comment: 17 pages, LaTeX, and one figur

Stress-Energy Tensor for the Massless Spin 1/2 Field in Static Black Hole Spacetimes

The stress-energy tensor for the massless spin 1/2 field is numerically computed outside and on the event horizons of both charged and uncharged static non-rotating black holes, corresponding to the Schwarzschild, Reissner-Nordstrom and extreme Reissner-Nordstr\"om solutions of Einstein's equations. The field is assumed to be in a thermal state at the black hole temperature. Comparison is made between the numerical results and previous analytic approximations for the stress-energy tensor in these spacetimes. For the Schwarzschild (charge zero) solution, it is shown that the stress-energy differs even in sign from the analytic approximation. For the Reissner-Nordstrom and extreme Reissner-Nordstrom solutions, divergences predicted by the analytic approximations are shown not to exist.Comment: 5 pages, 4 figures, additional discussio

Predictors of physical activity in older adults early in an emergency hospital admission: a prospective cohort study.

BACKGROUND: Reduced mobility may be responsible for functional decline and acute sarcopenia in older hospitalised patients. The drivers of reduced in-hospital mobility are poorly understood, especially during the early phase of acute hospitalisation. We investigated predictors of in-hospital activity during a 24-h period in the first 48 h of hospital admission in older adults. METHODS: This was a secondary analysis of a prospective repeated measures cohort study. Participants aged 75 years or older were recruited within the first 24 h of admission. At recruitment, patients underwent a baseline assessment including measurements of pre-morbid functional mobility, cognition, frailty, falls efficacy, co-morbidity, acute illness severity, knee extension strength and grip strength, and consented to wear accelerometers to measure physical activity during the first 7 days (or until discharge if earlier). In-hospital physical activity was defined as the amount of upright time (standing or walking). To examine the predictors of physical activity, we limited the analysis to the first 24 h of recording to maximise the sample size as due to discharge from hospital there was daily attrition. We used a best subset analysis including all baseline measures. The optimal model was defined by having the lowest Bayesian information criterion in the best-subset analyses. The model specified a maximum of 5 covariates and used an exhaustive search. RESULTS: Seventy participants were recruited but eight were excluded from the final analysis due to lack of accelerometer data within the first 24 h after recruitment. Patients spent a median of 0.50 h (IQR: 0.21; 1.43) standing or walking. The optimal model selected the following covariates: functional mobility as measured by the de Morton Mobility Index and two measures of illness severity, the National Early Warning Score, and serum C-reactive protein. CONCLUSIONS: Physical activity, particularly in the acute phase of hospitalisation, is very low in older adults. The association between illness severity and physical activity may be explained by symptoms of acute illness being barriers to activity. Interdisciplinary approaches are required to identify early mobilisation opportunities

Generic effective source for scalar self-force calculations

A leading approach to the modelling of extreme mass ratio inspirals involves the treatment of the smaller mass as a point particle and the computation of a regularized self-force acting on that particle. In turn, this computation requires knowledge of the regularized retarded field generated by the particle. A direct calculation of this regularized field may be achieved by replacing the point particle with an effective source and solving directly a wave equation for the regularized field. This has the advantage that all quantities are finite and require no further regularization. In this work, we present a method for computing an effective source which is finite and continuous everywhere, and which is valid for a scalar point particle in arbitrary geodesic motion in an arbitrary background spacetime. We explain in detail various technical and practical considerations that underlie its use in several numerical self-force calculations. We consider as examples the cases of a particle in a circular orbit about Schwarzschild and Kerr black holes, and also the case of a particle following a generic time-like geodesic about a highly spinning Kerr black hole. We provide numerical C code for computing an effective source for various orbital configurations about Schwarzschild and Kerr black holes.Comment: 24 pages, 7 figures, final published versio

Diagnosis of Metastatic Breast Cancer to an Intraabdominal Lymph Node by Endoscopic Ultrasound

Breast cancer can present with metastatic disease initially or as a systemic relapse despite seemingly adequate initial treatment. We report a case of suspected metastatic breast cancer to an intraabdominal lymph node based on imaging, which was subsequently confirmed by tissue sampling at the time of endoscopic ultrasound (EUS). While previous studies have shown the utility of EUS in the diagnosis of metastatic breast cancer, this is the first case to our knowledge that describes the use of EUS in diagnosing recurrent breast cancer to an intraabdominal lymph node

A Geometrical Approach to Strong Gravitational Lensing in f(R) Gravity

We present a framework for the study of lensing in spherically symmetric spacetimes within the context of f(R) gravity. Equations for the propagation of null geodesics, together with an expression for the bending angle are derived for any f(R) theory and then applied to an exact spherically symmetric solution of R^n gravity. We find that for this case more bending is expected for R^n gravity theories in comparison to GR and is dependent on the value of n and the value of distance of closest approach of the incident null geodesic.Comment: 9 page

Concatenation and Concordance in the Reconstruction of Mouse Lemur Phylogeny: An Empirical Demonstration of the Effect of Allele Sampling in Phylogenetics

The systematics and speciation literature is rich with discussion relating to the potential for gene tree/species tree discordance. Numerous mechanisms have been proposed to generate discordance, including differential selection, longbranch attraction, gene duplication, genetic introgression, and/or incomplete lineage sorting. For speciose clades in which divergence has occurred recently and rapidly, recovering the true species tree can be particularly problematic due to incomplete lineage sorting. Unfortunately, the availability of multilocus or “phylogenomic” data sets does not simply solve the problem, particularly when the data are analyzed with standard concatenation techniques. In our study, we conduct a phylogenetic study for a nearly complete species sample of the dwarf and mouse lemur clade, Cheirogaleidae. Mouse lemurs (genus, Microcebus) have been intensively studied over the past decade for reasons relating to their high level of cryptic species diversity, and although there has been emerging consensus regarding the evolutionary diversity contained within the genus, there is no agreement as to the inter-specific relationships within the group. We attempt to resolve cheirogaleid phylogeny, focusing especially on the mouse lemurs, by employing a large multilocus data set. We compare the results of Bayesian concordance methods with those of standard gene concatenation, finding that though concatenation yields the strongest results as measured by statistical support, these results are found to be highly misleading. By employing an approach where individual alleles are treated as operational taxonomic units, we show that phylogenetic results are substantially influenced by the selection of alleles in the concatenation process. Includes supplementary materials