The non-perturbative BRST quartet mechanism in Landau gauge QCD: Ghost-gluon and ghost-quark bound states

The non-perturbative BRST quartet mechanism in infrared Landau gauge QCD is presented. It is demonstrated that positivity violation for transverse gluons allows to identify the gluon's non-perturbative BRST quartet. To describe the respective BRST-daughter state a truncated Bethe-Salpeter equation for the gluon-ghost bound state is investigated. An analogous construction for quarks yields a truncated Bethe-Salpeter equation for the quark-ghost bound state. The gluon-ghost bound state equation in two space-time dimensions has been numerically solved.Comment: 3 pages, 1 figure; Poster presented at the Xth Quark Confinement and the Hadron Spectrum, Munich, Germany, 201

Algorithmic derivation of Dyson-Schwinger Equations

We present an algorithm for the derivation of Dyson-Schwinger equations of general theories that is suitable for an implementation within a symbolic programming language. Moreover, we introduce the Mathematica package DoDSE which provides such an implementation. It derives the Dyson-Schwinger equations graphically once the interactions of the theory are specified. A few examples for the application of both the algorithm and the DoDSE package are provided. The package can be obtained from physik.uni-graz.at/~mah/DoDSE.html.Comment: 17 pages, 11 figures, downloadable Mathematica package v2: adapted to version 1.2 of DoDSE package with simplified handling and improved plotting of graphs; references adde

Asymptotically Safe f(R)f(R)-Gravity Coupled to Matter II: Global Solutions

Ultraviolet fixed point functions of the functional renormalisation group equation for $f(R)$-gravity coupled to matter fields are discussed. The metric is split via the exponential parameterisation into a background and a fluctuating metric, the former is chosen to be the one of a four-sphere. Also when scalar, fermion and vector fields are included global quadratic solutions exist as in the pure gravity case for discrete sets of values for some endomorphism parameters defining the coarse-graining scheme. The asymptotic, large-curvature behaviour of the fixed point functions is analysed for generic values of these parameters. Examples for global numerical solutions are provided. A special focus is given to the question whether matter fields might destabilise the ultraviolet fixed point function. Similar to a previous analysis of a polynomial, small-curvature approximation to the fixed point functions different classes for such functions are found.Comment: 12 pages, 2 figure

Extraction of Spectral Functions from Dyson-Schwinger Studies via the Maximum Entropy Method

It is shown how to apply the Maximum Entropy Method (MEM) to numerical Dyson-Schwinger studies for the extraction of spectral functions of correlators from their corresponding Euclidean propagators. Differences to the application in lattice QCD are emphasized and, as an example, the spectral functions of massless quarks in cold and dense matter are presented.Comment: 16 pages, 7 figure

Octet and Decuplet Baryons in a Confining and Covariant Diquark-Quark Model

We treat baryons as bound states of scalar or axialvector diquarks and a constituent quark which interact through quark exchange. We obtain fully four-dimensional wave functions for both octet and decuplet baryons as solutions of the corresponding Bethe-Salpeter equation. Applications currently under investigation are: electromagnetic and strong form factors and strangeness production processes.Comment: 4 pages, 1 figure; talk given by R. Alkofer at PANIC 9

The effect of an infrared divergent quark-antiquark interaction kernel on other Green functions

The n-point Green functions of Landau gauge QCD are systematically investigated in a Dyson-Schwinger approach assuming a static linearly rising potential between fundamental color charges. Besides quarks also scalar matter in the fundamental representation is considered. Starting from the hypothesis of an 1/k^4 infrared divergent matter-antimatter vertex restrictions on the general color tensor structure of this divergence are derived. Consequences for the other four-point functions of QCD, resp., scalar QCD, are presented. Hereby Casimir scaling is found. It is shown that possible singular contributions to the three-point functions vanish due to cancellations within the color algebra. On the other hand, higher n-point functions inherit the infrared singularity of the matter-antimatter vertex in certain color channels. The presented results show that linear confinement is consistently possible in a Greens function approach, however, at the expense that the decoupling theorem is circumvented by infrared singularities.Comment: 7 pages, 2figures, talk presented at the Xth Quark Confinement and the Hadron Spectrum, Munich, Germany, 201