Extended Iterative Scheme for QCD: Three-point Vertices

In the framework of a generalized iterative scheme introduced previously to account for the non-analytic coupling dependence associated with the renormalization-group invariant mass scale Lambda, we establish the self-consistency equations of the extended Feynman rules (Lambda-modified vertices of zeroth perturbative order) for the three-gluon vertex, the two ghost vertices, and the two vertices of massless quarks. Calculations are performed to one-loop-order, in Landau gauge, and at the lowest approximation level (r=1) of interest for QCD. We discuss the phenomenon of compensating poles inherent in these equations, by which the formalism automatically cancels unphysical poles on internal lines, and the role of composite-operator information in the form of equation-of-motion condensate conditions. The observed near decoupling of the four-gluon conditions permits a solution to the 2-and-3-point conditions within an effective one-parameter freedom. There exists a parameter range in which one solution has all vertex coefficients real, as required for a physical solution, and a narrower range in which the transverse-gluon and massless-quark propagators both exhibit complex-conjugate pole pairs.Comment: 28 pages, 7 figure

Koedukativer Sportunterricht aus Sicht tänzerisch aktiver Schülerinnen

Czyrnick-Leber U, Batdorf D, Kuhrs MJ, Kleigrewe L, Lause J, Quiering M. Koedukativer Sportunterricht aus Sicht tänzerisch aktiver Schülerinnen. In: Langer W, Bähr I, Gerlach E, Krieger C, Walter M, Universität Hamburg, eds. Sportpädagogik - Der Sitzplatz zwischen den Stühlen?! . Hamburg: Hamburg: 61; 2023

In situ Characterisation of Practical Heterogeneous Catalysts

In situ methods are considered as a curiosity within the standard methodology of practical catalyst characterization. The methods are not commercially available and need to be adapted and validated for each specific problem. The great advantage of these methods is, however, that they deliver immediately relevant characteristics of the working state of a heterogeneous catalyst and allow justified structure-function relations to be deduced. To achieve this it is essential that the experiments are planned and conducted in such away that the proven to be active state of the catalyst is investigated. This can only be ascertained if simultaneous kinetic and spectroscopic data are acquired. The contribution lists a selection of methods with their main characteristics that allows to choose from the wide spectrum of information those that are most relevant for the given problem. A tabulated selection of case studies from the literature gives some insight in the current practice