Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Hot Flat Space and Gaussian Approximation in the Optical Schwarzschild Metric

Continuing our investigation of the regularization of the noise kernel in curved spacetimes [N. G. Phillips and B. L. Hu, Phys. Rev. D {\bf 63}, 104001 (2001)] we adopt the modified point separation scheme for the class of optical spacetimes using the Gaussian approximation for the Green functions a la Bekenstein-Parker-Page. In the first example we derive the regularized noise kernel for a thermal field in flat space. It is useful for black hole nucleation considerations. In the second example of an optical Schwarzschild spacetime we obtain a finite expression for the noise kernel at the horizon and recover the hot flat space result at infinity. Knowledge of the noise kernel is essential for studying issues related to black hole horizon fluctuations and Hawking radiation backreaction. We show that the Gaussian approximated Green function which works surprisingly well for the stress tensor at the Schwarzschild horizon produces significant error in the noise kernel there. We identify the failure as occurring at the fourth covariant derivative order.Comment: 21 pages, RevTeX

The development and initial validation of the Breast Cancer Recurrence instrument (BreastCaRe)—a patient-reported outcome measure for detecting symptoms of recurrence after breast cancer

Purpose: Patient-reported outomes (PRO) may facilitate prompt treatment. We describe the development and psychometric properties of the first instrument to monitor for symptoms of breast cancer (BC) recurrence. Methods: This study is nested in the MyHealth randomized trial of nurse-led follow-up based on electronically-collected PROs. We constructed items assessing symptoms of potential recurrence through expert interviews with six BC specialists in Denmark. Semi-structured cognitive interviews were carried out with a patient panel to assess acceptability and comprehensibility. Items were subsequently tested in a population of 1170 women 1–10 years after completing BC treatment. We carried out multiple-groups confirmatory factor analysis (CFA) and Rasch analysis to test dimensionality, local dependence (LD) and differential item functioning (DIF) according to sociodemographic and treatment-related factors. Clinical data was obtained from the Danish Breast Cancer Group registry. Results: Twenty-two items were generated for the Breast Cancer Recurrence instrument (BreastCaRe). Cognitive testing resulted in clearer items. Seven subscales based on general, bone, liver, lung, brain, locoregional and contralateral recurrence symptoms were proposed. Both CFA and Rasch models confirmed the factor structure. No DIF was identified. Five item pairs showed LD but all items were retained to avoid loss of clinical information. Rasch models taking LD into account were used to generate a standardized scoring table for each subscale. Conclusions: The BreastCaRe has good content and structural validity, patient acceptability and measurement invariance. We are preparing to examine the predictive validity of this new instrument

Calcium, vitamin D, casein and whey protein intakes and periodontitis among Danish adults

Objective: To investigate whether intakes of Ca, vitamin D, casein and whey are associated with periodontitis and to investigate the possibility of interactions between them. Design: Cross-sectional study. An Internet-based, 267-item FFQ was used to assess dietary intake. Intakes of casein (32·0 g/d), whey proteins (9·6 g/d) and vitamin D (5·8 μg/d) were classified as within v. above the 50th percentile. Ca intake was classified as within v. below age-specific recommendations. Severe periodontitis was defined as having ≥2 inter-proximal sites with clinical attachment loss ≥6 mm (not on the same tooth) and ≥1 inter-proximal site with pocket depth ≥5 mm. Since vitamin D influences Ca absorption, models were stratified by lower and higher (<5·8 v. ≥5·8 µg/d) vitamin D intake. Setting: Danish Health Examination Survey (DANHES) 2007–2008. Subjects: Adult participants (n 3287) in the oral health study of DANHES 2007–2008. Results: Intakes of Ca within recommendations (OR=0·76; 95 % CI 0·58, 0·99), whey ≥9·6 g/d (OR=0·75; 95 % CI 0·58, 0·97) and casein ≥32 g/d (OR=0·75 95 % CI 0·58, 0·97) were associated with lower likelihood of severe periodontitis after adjustment for age, gender, education, smoking, sucrose intake, alcohol consumption, number of teeth, daily brushing, regular visits to the dentist and chronic illness, irrespective of vitamin D intake levels. Intake of vitamin D alone was not associated severe with periodontitis. Conclusions: Intakes of Ca, casein and whey protein were inversely associated with periodontitis. Consumption of foods rich in Ca, casein and whey (e.g. dairy foods) should be promoted, as they may contribute to the prevention of periodontitis. Further longitudinal studies are required to confirm these associations

Prospects for asteroseismology

The observational basis for asteroseismology is being dramatically strengthened, through more than two years of data from the CoRoT satellite, the flood of data coming from the Kepler mission and, in the slightly longer term, from dedicated ground-based facilities. Our ability to utilize these data depends on further development of techniques for basic data analysis, as well as on an improved understanding of the relation between the observed frequencies and the underlying properties of the stars. Also, stellar modelling must be further developed, to match the increasing diagnostic potential of the data. Here we discuss some aspects of data interpretation and modelling, focussing on the important case of stars with solar-like oscillations.Comment: Proc. HELAS Workshop on 'Synergies between solar and stellar modelling', eds M. Marconi, D. Cardini & M. P. Di Mauro, Astrophys. Space Sci., in the press Revision: correcting abscissa labels on Figs 1 and

Three-Body Halos. II. from Two- to Three-Body Asymptotics

The large distance behavior of weakly bound three-body systems is investigated. The Schr\"{o}dinger equation and the Faddeev equations are reformulated by an expansion in eigenfunctions of the angular part of a corresponding operator. The resulting coupled set of effective radial equations are then derived. Both two- and three-body asymptotic behavior are possible and their relative importance is studied for systems where subsystems may be bound. The system of two nucleons outside a core is studied numerically in detail and the character of possible halo structure is pointed out and investigated.Comment: 16 pages, compressed and uuencoded PosrScript file, IFA-94/3

Fluctuations of the vacuum energy density of quantum fields in curved spacetime via generalized zeta functions

For quantum fields on a curved spacetime with an Euclidean section, we derive a general expression for the stress energy tensor two-point function in terms of the effective action. The renormalized two-point function is given in terms of the second variation of the Mellin transform of the trace of the heat kernel for the quantum fields. For systems for which a spectral decomposition of the wave opearator is possible, we give an exact expression for this two-point function. Explicit examples of the variance to the mean ratio $\Delta' = (-^2)/(^2)$ of the vacuum energy density $\rho$ of a massless scalar field are computed for the spatial topologies of $R^d\times S^1$ and $S^3$, with results of $\Delta'(R^d\times S^1) =(d+1)(d+2)/2$, and $\Delta'(S^3) = 111$ respectively. The large variance signifies the importance of quantum fluctuations and has important implications for the validity of semiclassical gravity theories at sub-Planckian scales. The method presented here can facilitate the calculation of stress-energy fluctuations for quantum fields useful for the analysis of fluctuation effects and critical phenomena in problems ranging from atom optics and mesoscopic physics to early universe and black hole physics.Comment: Uses revte

One loop renormalization of the four-dimensional theory for quantum dilaton gravity.

We study the one loop renormalization in the most general metric-dilaton theory with the second derivative terms only. The general theory can be divided into two classes, models of one are equivalent to conformally coupled with gravity scalar field and also to general relativity with cosmological term. The models of second class have one extra degree of freedom which corresponds to dilaton. We calculate the one loop divergences for the models of second class and find that the arbitrary functions of dilaton in the starting action can be fine-tuned in such a manner that all the higher derivative counterterms disappear on shell. The only structures in both classical action and counterterms, which survive on shell, are the potential (cosmological) ones. They can be removed by renormalization of the dilaton field which acquire the nontrivial anomalous dimension, that leads to the effective running of the cosmological constant. For some of the renormalizable solutions of the theory the observable low energy value of the cosmological constant is small as compared with the Newtonian constant. We also discuss another application of our result.Comment: 21 pages, latex, no figures

Bianchi VIIAVII_A solutions of quadratic gravity

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "open" model $H^ 3$ for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain way. It is found solutions which asymptote de Sitter space, Riemann flat space and a singularity. The question of isotropisation of an initially anisotropic Universe is of great importance in the context of cosmology. Although isotropisation is not directly discussed in this present work, we show that sufficiently small anisotropies, do not increase indefinitely according to particular quadratic gravity theories. It can be understood as weak isotropisation, and we stress that this result is strongly dependent on initial conditions.Comment: version accepted for publication in General Relativity and Gravitation. arXiv admin note: substantial text overlap with arXiv:1203.688

Extreme magnification of an individual star at redshift 1.5 by a galaxy-cluster lens

Galaxy-cluster gravitational lenses can magnify background galaxies by a total factor of up to ~50. Here we report an image of an individual star at redshift z = 1.49 (dubbed MACS J1149 Lensed Star 1) magnified by more than ×2,000. A separate image, detected briefly 0.26″ from Lensed Star 1, is probably a counterimage of the first star demagnified for multiple years by an object of ≳3 solar masses in the cluster. For reasonable assumptions about the lensing system, microlensing fluctuations in the stars’ light curves can yield evidence about the mass function of intracluster stars and compact objects, including binary fractions and specific stellar evolution and supernova models. Dark-matter subhaloes or massive compact objects may help to account for the two images’ long-term brightness ratio