Infrared divergence in QED3_3 at finite temperature

We consider various ways of treating the infrared divergence which appears in the dynamically generated fermion mass, when the transverse part of the photon propagator in N flavour $QED_{3}$ at finite temperature is included in the Matsubara formalism. This divergence is likely to be an artefact of taking into account only the leading order term in the $1 \over N$ expansion when we calculate the photon propagator and is handled here phenomenologically by means of an infrared cutoff. Inserting both the longitudinal and the transverse part of the photon propagator in the Schwinger-Dyson equation we find the dependence of the dynamically generated fermion mass on the temperature and the cutoff parameters. It turns out that consistency with certain statistical physics arguments imposes conditions on the cutoff parameters. For parameters in the allowed range of values we find that the ratio $r=2*Mass(T=0)/critical temperature$ is approximately 6, consistently with previous calculations which neglected the transverse photon contribution.Comment: 37 pages, 12 figures, typos corrected, references added, Introduction rewritte

Randomised controlled trial of homoeopathy versus placebo in perennial allergic rhinitis with overview of four trial series

OBJECTIVE: To test the hypothesis that homoeopathy is a placebo by examining its effect in patients with allergic rhinitis and so contest the evidence from three previous trials in this series. Design: Randomised, double blind, placebo controlled, parallel group, multicentre study. SETTING: Four general practices and a hospital ear, nose, and throat outpatient department. PARTICIPANTS: 51 patients with perennial allergic rhinitis. Intervention: Random assignment to an oral 30c homoeopathic preparation of principal inhalant allergen or to placebo. MAIN OUTCOME MEASURES: Changes from baseline in nasal inspiratory peak flow and symptom visual analogue scale score over third and fourth weeks after randomisation. RESULTS: Fifty patients completed the study. The homoeopathy group had a significant objective improvement in nasal airflow compared with the placebo group (mean difference 19.8 l/min, 95% confidence interval 10.4 to 29.1, P=0.0001). Both groups reported improvement in symptoms, with patients taking homoeopathy reporting more improvement in all but one of the centres, which had more patients with aggravations. On average no significant difference between the groups was seen on visual analogue scale scores. Initial aggravations of rhinitis symptoms were more common with homoeopathy than placebo (7 (30%) v 2 (7%), P=0.04). Addition of these results to those of three previous trials (n=253) showed a mean symptom reduction on visual analogue scores of 28% (10.9 mm) for homoeopathy compared with 3% (1.1 mm) for placebo (95% confidence interval 4.2 to 15.4, P=0.0007). CONCLUSION: The objective results reinforce earlier evidence that homoeopathic dilutions differ from placebo

On dynamical mass generation in three dimensional supersymmetric U(1) gauge field theory

We investigate and contrast the non-perturbative infra red structure of N=1 and N=2 supersymmetric non-compact U(1) gauge field theory in three space-time dimensions with N matter flavours. We study the Dyson-Schwinger equations in a general gauge using superfield formalism; this ensures that supersymmetry is kept manifest, though leads to spurious infra red divergences which we have to avoid carefully. In the N=1 case the superfield formalism allows us to choose a vertex which satisfies the U(1) Ward identity exactly, and we find the expected critical behaviour in the wavefunction renormalization and strong evidence for the existence of a gauge independent dynamically generated mass, but with no evidence for a critical flavour number. We study the N=2 model by dimensional reduction from four dimensional N=1 electrodynamics, and we refine the old gauge dependence argument that there is no dynamical mass generation. We recognize that the refinement only holds after dimensional reduction.Comment: 32 pages RevTeX; 3 axodraw figures include

Non-trivial Infrared Structure in (2+1)-dimensional Quantum Electrodynamics

We show that the gauge-fermion interaction in multiflavour $(2+1)$-dimensional quantum electrodynamics with a finite infrared cut-off is responsible for non-fermi liquid behaviour in the infrared, in the sense of leading to the existence of a non-trivial fixed point at zero momentum, as well as to a significant slowing down of the running of the coupling at intermediate scales as compared with previous analyses on the subject. Both these features constitute deviations from fermi-liquid theory. Our discussion is based on the leading- $1/N$ resummed solution for the wave-function renormalization of the Schwinger-Dyson equations . The present work completes and confirms the expectations of an earlier work by two of the authors (I.J.R.A. and N.E.M.) on the non-trivial infrared structure of the theory.Comment: 10 pages (LaTex), 5 figures (Postscript

\u3ci\u3e On the flora of the Kuram Valley &c., Afghanistan\u3c/i\u3e

The collection of plants was made during the summer of 1879 in Afghanistan territory, along the left bank of he Kuram river from Thal to Pewar kotal. It consists of 15,000 specimens, belonging to 950 species

Dynamical Mass Generation in a Finite-Temperature Abelian Gauge Theory

We write down the gap equation for the fermion self-energy in a finite-temperature abelian gauge theory in three dimensions. The instantaneous approximation is relaxed, momentum-dependent fermion and photon self-energies are considered, and the corresponding Schwinger-Dyson equation is solved numerically. The relation between the zero-momentum and zero-temperature fermion self-energy and the critical temperature T_c, above which there is no dynamical mass generation, is then studied. We also investigate the effect which the number of fermion flavours N_f has on the results, and we give the phase diagram of the theory with respect to T and N_f.Comment: 20 LaTeX pages, 4 postscript figures in a single file, version to appear in Physical Review

Finiteness properties of cubulated groups

We give a generalized and self-contained account of Haglund-Paulin's wallspaces and Sageev's construction of the CAT(0) cube complex dual to a wallspace. We examine criteria on a wallspace leading to finiteness properties of its dual cube complex. Our discussion is aimed at readers wishing to apply these methods to produce actions of groups on cube complexes and understand their nature. We develop the wallspace ideas in a level of generality that facilitates their application. Our main result describes the structure of dual cube complexes arising from relatively hyperbolic groups. Let H_1,...,H_s be relatively quasiconvex codimension-1 subgroups of a group G that is hyperbolic relative to P_1,...,P_r. We prove that G acts relatively cocompactly on the associated dual CAT(0) cube complex C. This generalizes Sageev's result that C is cocompact when G is hyperbolic. When P_1,...,P_r are abelian, we show that the dual CAT(0) cube complex C has a G-cocompact CAT(0) truncation.Comment: 58 pages, 12 figures. Version 3: Revisions and slightly improved results in Sections 7 and 8. Several theorem numbers have changed from the previous versio

Measuring visual cortical oxygenation in diabetes using functional near-infrared spectroscopy

Aims: Diabetes mellitus affects about 6% of the world’s population, and the chronic complications of the disease may result in macro- and micro-vascular changes. The purpose of the current study was to shed light on visual cortical oxygenation in diabetic individuals. We then aimed to compare the haemodynamic response (HDR) to visual stimulation with glycaemic control, given the likelihood of diabetic individuals suffering from such macro- and micro-vascular insult. Methodology: Thirty participants took part in this explorative study, fifteen of whom had diabetes and fifteen of whom were non-diabetic controls. The HDR, measured as concentrations of oxyhaemoglobin [HbO] and deoxyhaemoglobin [HbR], to visual stimulation was recorded over the primary visual cortex (V1) using a dual-channel oximeter. The stimulus comprised a pattern-reversal checkerboard presented in a block design. Participants’ mean glycated haemoglobin (HbA1c) level (±SD) was 7.2±0.6% in the diabetic group and 5.5±0.4% in the non-diabetic group. Raw haemodynamic data were normalised to baseline, and the last 15 s of data from each ‘stimulus on’ and ‘stimulus off’ condition were averaged over seven duty cycles for each participant. Results: There were statistically significant differences in ∆[HbO] and ∆[HbR] to visual stimulation between diabetic and non-diabetic groups (p<0.05). In the diabetic group, individuals with type 1 diabetes displayed an increased [HbO] (p<0.01) and decreased [HbR] (p<0.05) compared to their type 2 counterparts. There was also a linear relationship between both ∆[HbO] and ∆[HbR] as a function of HbA1c level (p<0.0005). Conclusions: Our findings suggest that fNIRS can be used as a quantitative measure of cortical oxygenation in diabetes. Diabetic individuals have a larger HDR to visual stimulation compared to non-diabetic individuals. This increase in ∆[HbO] and decrease in ∆[HbR] appears to be correlated with HbA1c level