Functional Renormalization Group Methods in Quantum Chromodynamics

We apply functional Renormalization Group methods to Quantum Chromodynamics (QCD). First we calculate the mass shift for the pion in a finite volume in the framework of the quark-meson model. In particular, we investigate the importance of quark effects. As in lattice gauge theory, we find that the choice of quark boundary conditions has a noticeable effect on the pion mass shift in small volumes. A comparison of our results to chiral perturbation theory and lattice QCD suggests that lattice QCD has not yet reached volume sizes for which chiral perturbation theory can be applied to extrapolate lattice results for low-energy observables. Phase transitions in QCD at finite temperature and density are currently very actively researched. We study the chiral phase transition at finite temperature with two approaches. First, we compute the phase transition temperature in infinite and in finite volume with the quark-meson model. Though qualitatively correct, our results suggest that the model does not describe the dynamics of QCD near the finite-temperature phase boundary accurately. Second, we study the approach to chiral symmetry breaking in terms of quarks and gluons. We compute the running QCD coupling for all temperatures and scales. We use this result to determine quantitatively the phase boundary in the plane of temperature and number of quark flavors and find good agreement with lattice results.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Heidelberg

Year

2006

Author dc:creator

• Braun, Jens

Contributors dc:contributor

• Pirner, Hans-Jürgen

Repository record source_url

http://www.ub.uni-heidelberg.de/archiv/7040

OAI identifier oai:identifier

oai:archiv.ub.uni-heidelberg.de:7040