Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory

The infrared behaviour of vertex functions in an SU(N) Yang-Mills theory in Landau gauge is investigated employing a skeleton expansion of the Dyson-Schwinger equations. The three- and four-gluon vertices become singular if and only if all external momenta vanish while the dressing of the ghost-gluon vertex remains finite in this limit. The running coupling as extracted from either of these vertex functions possesses an infrared fixed point. In general, diagrams including ghost-loops dominate in the infrared over purely gluonic ones.Comment: 14 pages, 8 figures, v2: typos corrected, version to be published in PL

Renormalization flow of Yang-Mills propagators

We study Landau-gauge Yang-Mills theory by means of a nonperturbative vertex expansion of the quantum effective action. Using an exact renormalization group equation, we compute the fully dressed gluon and ghost propagators to lowest nontrivial order in the vertex expansion. In the mid-momentum regime, $p^2\sim\mathcal{O}(1)\text{GeV}^2$, we probe the propagator flow with various {\em ans\"atze} for the three- and four-point correlations. We analyze the potential of these truncation schemes to generate a nonperturbative scale. We find universal infrared behavior of the propagators, if the gluon dressing function has developed a mass-like structure at mid-momentum. The resulting power laws in the infrared support the Kugo-Ojima confinement scenario.Comment: 28 pages, 5 figures. V2: Typos corrected and reference adde

Improved lower bounds for the ground-state energy of many-body systems

New lower bounds for the binding energy of a quantum-mechanical system of interacting particles are presented. The new bounds are expressed in terms of two-particle quantities and improve the conventional bounds of the Hall-Post type. They are constructed by considering not only the energy in the two-particle system, but also the structure of the pair wave function. We apply the formal results to various numerical examples, and show that in some cases dramatic improvement over the existing bounds is reached.Comment: 29 pages, 5 figures, to be published in Phys. Rev.

Solution of coupled vertex and propagator Dyson-Schwinger equations in the scalar Munczek-Nemirovsky model

In a scalar $\phi^2\chi$ model, we exactly solve the vertex and $\phi$ propagator Dyson-Schwinger equations under the assumption of a spatially constant (Munczek-Nemirovsky) propagator for the $\chi$ field. Various truncation schemes are also considered.Comment: 7 pages,4 figures, minor changes, reference added for published versio

αs\alpha_s from τ\tau decays: contour-improved versus fixed-order summation in a new QCD perturbation expansion

We consider the determination of $\alpha_s$ from $\tau$ hadronic decays, by investigating the contour-improved (CI) and the fixed-order (FO) renormalization group summations in the frame of a new perturbation expansion of QCD, which incorporates in a systematic way the available information about the divergent character of the series. The new expansion functions, which replace the powers of the coupling, are defined by the analytic continuation in the Borel complex plane, achieved through an optimal conformal mapping. Using a physical model recently discussed by Beneke and Jamin, we show that the new CIPT approaches the true results with great precision when the perturbative order is increased, while the new FOPT gives a less accurate description in the regions where the imaginary logarithms present in the expansion of the running coupling are large. With the new expansions, the discrepancy of 0.024 in $\alpha_s(m_\tau^2)$ between the standard CI and FO summations is reduced to only 0.009. From the new CIPT we predict $\alpha_s(m_\tau^2)= 0.320 ^{+0.011}_{-0.009}$, which practically coincides with the result of the standard FOPT, but has a more solid theoretical basis

On an asymptotic estimate of the nn-loop correction in perturbative QCD

A recently proposed method of estimating the asymptotic behaviour of QCD perturbation theory coefficients is critically reviewed and shown to contain numerous invalid mathematical operations and unsubstantiated assumptions. We discuss in detail why this procedure, based solely on renormalization group (RG) considerations and analyticity constraints, cannot lead to such estimates. We stress the importance of correct renormalization scheme (RS) dependence of any meaningful asymptotic estimate and argue that the unambiguous summation of QCD perturbation expansions for physical quantities requires information from outside of perturbation theory itself.Comment: PRA-HEP-92/17, Latex, 20 pages of text plus 5 figures contained in 5 separate PS files. Four of them (corresponding to Figs.1,2,3,5) are appended at the end of this file, the (somewhat larger one) corresponding to Fig.4 can be obtained from any of the mentioned E-mail addresses upon request. E-mail connections: J. Chyla - [email protected]) or h1kchy@dhhdesy3 P. Kolar - [email protected]

On the black hole limit of rotating discs and rings

Solutions to Einstein's field equations describing rotating fluid bodies in equilibrium permit parametric (i.e. quasi-stationary) transitions to the extreme Kerr solution (outside the horizon). This has been shown analytically for discs of dust and numerically for ring solutions with various equations of state. From the exterior point of view, this transition can be interpreted as a (quasi) black hole limit. All gravitational multipole moments assume precisely the values of an extremal Kerr black hole in the limit. In the present paper, the way in which the black hole limit is approached is investigated in more detail by means of a parametric Taylor series expansion of the exact solution describing a rigidly rotating disc of dust. Combined with numerical calculations for ring solutions our results indicate an interesting universal behaviour of the multipole moments near the black hole limit.Comment: 18 pages, 4 figures; Dedicated to Gernot Neugebauer on the occasion of his 70th birthda

The TF Limit for Rapidly Rotating Bose Gases in Anharmonic Traps

Starting from the full many body Hamiltonian we derive the leading order energy and density asymptotics for the ground state of a dilute, rotating Bose gas in an anharmonic trap in the ` Thomas Fermi' (TF) limit when the Gross-Pitaevskii coupling parameter and/or the rotation velocity tend to infinity. Although the many-body wave function is expected to have a complicated phase, the leading order contribution to the energy can be computed by minimizing a simple functional of the density alone

Bounded version vectors

Version vectors play a central role in update tracking under optimistic distributed systems, allowing the detection of obsolete or inconsistent versions of replicated data. Version vectors do not have a bounded representation; they are based on integer counters that grow indefinitely as updates occur. Existing approaches to this problem are scarce; the mechanisms proposed are either unbounded or operate only under specific settings. This paper examines version vectors as a mechanism for data causality tracking and clarifies their role with respect to vector clocks. Then, it introduces bounded stamps and proves them to be a correct alternative to integer counters in version vectors. The resulting mechanism, bounded version vectors, represents the first bounded solution to data causality tracking between replicas subject to local updates and pairwise symmetrical synchronization.FCT project POSI/ICHS/44304/2002, FCT under grant BSAB/390/2003