Polaron Variational Methods In The Particle Representation Of Field Theory : II. Numerical Results For The Propagator

For the scalar Wick-Cutkosky model in the particle representation we perform a similar variational calculation for the 2-point function as was done by Feynman for the polaron problem. We employ a quadratic nonlocal trial action with a retardation function for which several ans\"atze are used. The variational parameters are determined by minimizing the variational function and in the most general case the nonlinear variational equations are solved numerically. We obtain the residue at the pole, study analytically and numerically the instability of the model at larger coupling constants and calculate the width of the dressed particle.Comment: 25 pages standard LaTeX, 9 uuencoded postscript figures embedded with psfig.st

Charged black holes: Wave equations for gravitational and electromagnetic perturbations

A pair of wave equations for the electromagnetic and gravitational perturbations of the charged Kerr black hole are derived. The perturbed Einstein-Maxwell equations in a new gauge are employed in the derivation. The wave equations refer to the perturbed Maxwell spinor $\Phi_0$ and to the shear $\sigma$ of a principal null direction of the Weyl curvature. The whole construction rests on the tripod of three distinct derivatives of the first curvature $\kappa$ of a principal null direction.Comment: 12 pages, to appear in Ap.

Non-Perturbative Mass Renormalization in Quenched QED from the Worldline Variational Approach

Following Feynman's successful treatment of the polaron problem we apply the same variational principle to quenched QED in the worldline formulation. New features arise from the description of fermions by Grassmann trajectories, the supersymmetry between bosonic and fermionic variables and the much more singular structure of a renormalizable gauge theory like QED in 3+1 dimensions. We take as trial action a general retarded quadratic action both for the bosonic and fermionic degrees of freedom and derive the variational equations for the corresponding retardation functions. We find a simple analytic, non-perturbative, solution for the anomalous mass dimension gamma_m(alpha) in the MS scheme. For small couplings we compare our result with recent four-loop perturbative calculations while at large couplings we find that gamma_m(alpha) becomes proportional to (alpha)^(1/2). The anomalous mass dimension shows no obvious sign of the chiral symmetry breaking observed in calculations based on the use of Dyson-Schwinger equations, however we find that a perturbative expansion of gamma_m(alpha) diverges for alpha > 0.7934. Finally, we investigate the behaviour of gamma_m(alpha) at large orders in perturbation theory.Comment: 18 pages, 1 Figure, RevTeX; the manuscript has been substantially revised and enlarged in order to make it selfcontained; accepted for publication in Phys. Rev.

Electromagnetic waves in NUT space: Solutions to the Maxwell equations

In this paper, using the Newman-Penrose formalism, we find the Maxwell equations in NUT space and after separation into angular and radial components solve them analytically. All the angular equations are solved in terms of Jaccobi polynomials. The radial equations are transformed into Hypergeometric and Heun's equations with the right hand sides including terms of different order in the frequency of the perturbation which allow solutions in the expansion of this parameter.Comment: 19 pages, Revtex format, Minor changes including an extention of the discussion and typos correction, (Extended version of the article presented to the GR16 conference, July 15-21 2001, Durban, South Africa

Identification of novel bile acids as biomarkers for the early diagnosis of Niemann-Pick C disease

This article describes a rapid UPLC-MS/MS method to quantitate novel bile acids in biological fluids and the evaluation of their diagnostic potential in Niemann-Pick C (NPC). Two new compounds, NPCBA1 (3β-hydroxy,7β-N-acetylglucosaminyl-5-cholenoic acid) and NPCBA2 (probably 3β,5α,6β-trihydroxycholanoyl-glycine), were observed to accumulate preferentially in NPC patients: median plasma concentrations of NPCBA1 and NPCBA2 were 40- and 10-fold higher in patients than in controls. However, NPCBA1 concentrations were normal in some patients because they carried a common mutation inactivating the GlcNAc transferase required for the synthesis of this bile acid. NPCBA2, not containing a GlcNAc moiety, is thus a better NPC biomarker

Nanostructured 3D Constructs Based on Chitosan and Chondroitin Sulphate Multilayers for Cartilage Tissue Engineering

Nanostructured three-dimensional constructs combining layer-by-layer technology (LbL) and template leaching were processed and evaluated as possible support structures for cartilage tissue engineering. Multilayered constructs were formed by depositing the polyelectrolytes chitosan (CHT) and chondroitin sulphate (CS) on either bidimensional glass surfaces or 3D packet of paraffin spheres. 2D CHT/CS multi-layered constructs proved to support the attachment and proliferation of bovine chondrocytes (BCH). The technology was transposed to 3D level and CHT/CS multi-layered hierarchical scaffolds were retrieved after paraffin leaching. The obtained nanostructured 3D constructs had a high porosity and water uptake capacity of about 300%. Dynamical mechanical analysis (DMA) showed the viscoelastic nature of the scaffolds. Cellular tests were performed with the culture of BCH and multipotent bone marrow derived stromal cells (hMSCs) up to 21 days in chondrogenic differentiation media. Together with scanning electronic microscopy analysis, viability tests and DNA quantification, our results clearly showed that cells attached, proliferated and were metabolically active over the entire scaffold. Cartilaginous extracellular matrix (ECM) formation was further assessed and results showed that GAG secretion occurred indicating the maintenance of the chondrogenic phenotype and the chondrogenic differentiation of hMSCs

Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model

We use the worldline representation of field theory together with a variational approximation to determine the lowest bound state in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons. Self-energy and vertex corrections are included approximately in a consistent way as well as crossed diagrams. Only vacuum-polarization effects of the heavy particles are neglected. In a path integral description of an appropriate current-current correlator an effective, retarded action is obtained by integrating out the meson field. As in the polaron problem we employ a quadratic trial action with variational functions to describe retardation and binding effects through multiple meson exchange.The variational equations for these functions are derived, discussed qualitatively and solved numerically. We compare our results with the ones from traditional approaches based on the Bethe-Salpeter equation and find an enhanced binding contrary to some claims in the literature. For weak coupling this is worked out analytically and compared with results from effective field theories. However, the well-known instability of the model, which usually is ignored, now appears at smaller coupling constants than in the one-body case and even when self-energy and vertex corrections are turned off. This induced instability is investigated analytically and the width of the bound state above the critical coupling is estimated.Comment: 62 pages, 7 figures, FBS style, published versio