Analytic structure of the Landau gauge gluon propagator

The analytic structure of the non-perturbative gluon propagator contains information on the absence of gluons from the physical spectrum of the theory. We study this structure from numerical solutions in the complex momentum plane of the gluon and ghost Dyson-Schwinger equations in Landau gauge Yang-Mills theory. The resulting ghost and gluon propagators are analytic apart from a distinct cut structure on the real, timelike momentum axis. The propagator violates the Osterwalder-Schrader positivity condition, confirming the absence of gluons from the asymptotic spectrum of the theory.Comment: 5 pages, 7 figure

On critical scaling at the QCD N_f=2 chiral phase transition

We investigate the critical scaling of the quark propagator of N_f=2 QCD close to the chiral phase transition at finite temperature. We argue that it is mandatory to take into account the back-reaction effects of pions and the sigma onto the quark to observe critical behavior beyond mean field. On condition of self-consistency of the quark Dyson-Schwinger equation we extract the scaling behavior for the quark propagator analytically. Crucial in this respect is the correct pion dispersion relation when the critical temperature is approached from below. Our results are consistent with the known relations for the quark condensate and the pion decay constant from universality. We verify the analytical findings also numerically assuming the critical dispersion relation for the Goldstone bosons.Comment: 9 pages, 6 figure

Chiral and deconfinement phase transitions of two-flavour QCD at finite temperature and chemical potential

We present results for the chiral and deconfinement transition of two flavor QCD at finite temperature and chemical potential. To this end we study the quark condensate and its dual, the dressed Polyakov loop, with functional methods using a set of Dyson-Schwinger equations. The quark-propagator is determined self-consistently within a truncation scheme including temperature and in-medium effects of the gluon propagator. For the chiral transition we find a crossover turning into a first order transition at a critical endpoint at large quark chemical potential, $\mu_{EP}/T_{EP} \approx 3$. For the deconfinement transition we find a pseudo-critical temperature above the chiral transition in the crossover region but coinciding transition temperatures close to the critical endpoint.Comment: 4 pages, 4 figures. v2: minor changes, comments adde

The Logic & Limits of the Exceptional Circumstances Test in Magill and IMS Health

In this Article, we show that, in contrast to the Commission\u27s balancing approach in Microsoft, the ECJ\u27s narrow construction of the obligation to license IP under Article 82 of the EC Treaty is based on sound economics and constitutes appropriate public policy. The set of “exceptional circumstances” listed in Magill and IMS Health constitutes a reasonable implementation of the optimal legal standard for the assessment of refusals to licence IP: modified per se legality. In the IP context, an obligation to make property available is a requirement for compulsory licensing. The ECJ test limits compulsory licensing to those situations in which the prospective social benefits of licensing are large, while the negative effects of reducing the incentives to innovate are small. The ECJ test ensures that intervention is restricted to cases where the intervention is still likely to increase social welfare. The Commission\u27s test in Microsoft, being a balancing test, does not. As noted by Professor Gerardin, “balancing ex ante vs. ex post efficiencies is obviously a very difficult process, which even the most sophisticated economists may find daunting. The risk of mistaken decisions is therefore high.

Quark spectral properties above Tc from Dyson-Schwinger equations

We report on an analysis of the quark spectral representation at finite temperatures based on the quark propagator determined from its Dyson-Schwinger equation in Landau gauge. In Euclidean space we achieve nice agreement with recent results from quenched lattice QCD. We find different analytical properties of the quark propagator below and above the deconfinement transition. Using a variety of ansaetze for the spectral function we then analyze the possible quasiparticle spectrum, in particular its quark mass and momentum dependence in the high temperature phase. This analysis is completed by an application of the Maximum Entropy Method, in principle allowing for any positive semi-definite spectral function. Our results motivate a more direct determination of the spectral function in the framework of Dyson-Schwinger equations