Gauge covariance and the fermion-photon vertex in three- and four- dimensional, massless quantum electrodynamics

In the quenched approximation, the gauge covariance properties of three vertex Ans\"{a}tze in the Schwinger-Dyson equation for the fermion self energy are analysed in three- and four- dimensional quantum electrodynamics. Based on the Cornwall-Jackiw-Tomboulis effective action, it is inferred that the spectral representation used for the vertex in the gauge technique cannot support dynamical chiral symmetry breaking. A criterion for establishing whether a given Ansatz can confer gauge covariance upon the Schwinger-Dyson equation is presented and the Curtis and Pennington Ansatz is shown to satisfy this constraint. We obtain an analytic solution of the Schwinger-Dyson equation for quenched, massless three-dimensional quantum electrodynamics for arbitrary values of the gauge parameter in the absence of dynamical chiral symmetry breaking.Comment: 17 pages, PHY-7143-TH-93, REVTE

The analytic structure of heavy quark propagators

The renormalised quark Dyson-Schwinger equation is studied in the limit of the renormalised current heavy quark mass m_R --> infinity. We are particularly interested in the analytic pole structure of the heavy quark propagator in the complex momentum plane. Approximations in which the quark-gluon vertex is modelled by either the bare vertex or the Ball-Chiu Ansatz, and the Landau gauge gluon propagator takes either a gaussian form or a gaussian form with an ultraviolet asymptotic tail are used.Comment: 21 pages Latex and 5 postscript figures. The original version of this paper has been considerably extended to include a formalism dealing with the renormalised heavy quark Dyson-Schwinger equation and uses a more realistic Ansatz for the gluon propagator

Vector Positronium States in QED3

The homogeneous Bethe-Salpeter equation is solved in the quenched ladder approximation for the vector positronium states of 4-component quantum electrodynamics in 2 space and 1 time dimensions. Fermion propagator input is from a Rainbow approximation Dyson-Schwinger solution, with a broad range of fermion masses considered. This work is an extension of earlier work on the scalar spectrum of the same model. The non-relativistic limit is also considered via the large fermion mass limit. Classification of states via their transformation properties under discrete parity transformations allows analogies to be drawn with the meson spectrum of QCD.Comment: 24 pages, 2 encapsulated postscript figure

Nonperturbative Vertices in Supersymmetric Quantum Electrodynamics

We derive the complete set of supersymmetric Ward identities involving only two- and three- point proper vertices in supersymmetric QED. We also present the most general form of the proper vertices consistent with both the supersymmetric and U(1) gauge Ward identities. These vertices are the supersymmetric equivalent of the non supersymmetric Ball-Chiu vertices.Comment: seventeen pages late

Characteristic value determination from small samples

The paper deals with the characteristic value determination from relatively small samples. When the distribution and its parameters of a random variable are known, the characteristic value is deterministic quantity. However, in practical problems the parameters of distribution are unknown and can only be estimated from random samples. Therefore the characteristic value is by itself a random variable. The estimates of characteristic values are strongly dependant on the distribution of random variable. In the paper we show the analytical solution for characteristic value determination from random samples of normal and lognormal random variables. The confirmation of analytical results is accomplished by the use of computer simulations. For Gumbel, and Weibull distribution the characteristic value estimates are obtained numerically by combination of simulations and bisection method. In the paper the numerical results are presented for 5% characteristic values with 75% confidence interval, which is in accord with the majority of European building standards. The proposed approach is demonstrated on the data of experimentally obtained bending strengths of finger jointed wooden beams. (C) 2006 Elsevier Ltd. All rights reserved

Exactly solvable strings in Minkowski spacetime

We study the integrability of the equations of motion for the Nambu-Goto strings with a cohomogeneity-one symmetry in Minkowski spacetime. A cohomogeneity-one string has a world surface which is tangent to a Killing vector field. By virtue of the Killing vector, the equations of motion can be reduced to the geodesic equation in the orbit space. Cohomogeneity-one strings are classified into seven classes (Types I to VII). We investigate the integrability of the geodesic equations for all the classes and find that the geodesic equations are integrable. For Types I to VI, the integrability comes from the existence of Killing vectors on the orbit space which are the projections of Killing vectors on Minkowski spacetime. For Type VII, the integrability is related to a projected Killing vector and a nontrivial Killing tensor on the orbit space. We also find that the geodesic equations of all types are exactly solvable, and show the solutions.Comment: 11 pages, a reference added, some points clarifie

QED in external fields, a functional point of view

A functional partial differential equation is set for the proper graphs generating functional of QED in external electromagnetic fields. This equation leads to the evolution of the proper graphs with the external field amplitude and the external field gauge dependence of the complete fermion propagator and vertex is derived non-perturbativally.Comment: 8 pages, published versio

Gauge covariant fermion propagator in quenched, chirally-symmetric quantum electrodynamics

We discuss the chirally symmetric solution of the massless, quenched, Dyson-Schwinger equation for the fermion propagator in three and four dimensions. The solutions are manifestly gauge covariant. We consider a gauge covariance constraint on the fermion--gauge-boson vertex, which motivates a vertex Ansatz that both satisfies the Ward identity when the fermion self-mass is zero and ensures gauge covariance of the fermion propagator.Comment: 11 pages. REVTEX 3.0. ANL-PHY-7711-TH-9

Pseudoscalar Meson Nonet at Zero and Finite Temperature

Theoretical understanding of experimental results from relativistic heavy-ion collisions requires a microscopic approach to the behavior of QCD n-point functions at finite temperatures, as given by the hierarchy of Dyson-Schwinger equations, properly generalized within the Matsubara formalism. The convergence of sums over Matsubara modes is studied. The technical complexity of finite-temperature calculations mandates modeling. We present a model where the QCD interaction in the infrared, nonperturbative domain, is modeled by a separable form. Results for the mass spectrum of light quark flavors (u, d, s) and for the pseudoscalar bound-state amplitudes at finite temperature are presented.Comment: 14 pages, 11 figures, accepted for publication in Physics of Particles and Nuclei Letters, based on invited lectures at "Dense Matter In Heavy Ion Collisions and Astrophysics", 21.08-01.09 2006, Dubna, Russi

Diquarks: condensation without bound states

We employ a bispinor gap equation to study superfluidity at nonzero chemical potential: mu .neq. 0, in two- and three-colour QCD. The two-colour theory, QC2D, is an excellent exemplar: the order of truncation of the quark-quark scattering kernel: K, has no qualitative impact, which allows a straightforward elucidation of the effects of mu when the coupling is strong. In rainbow-ladder truncation, diquark bound states appear in the spectrum of the three-colour theory, a defect that is eliminated by an improvement of K. The corrected gap equation describes a superfluid phase that is semi-quantitatively similar to that obtained using the rainbow truncation. A model study suggests that the width of the superfluid gap and the transition point in QC2D provide reliable quantitative estimates of those quantities in QCD.Comment: 7 pages, 3 figures, REVTEX, epsfi