Quark dynamics in the non-pertubative regime of quantum chromodynamics

The aim of this research project is a better understanding of the inner structure of matter in na-ture and of the strong interaction that binds its elementary constituents. Although the underlying theory, quantum chromodynamics, is known, it still lacks a thorough, microscopic explanation of the most basic aspects of matter. These fundamental properties like the confinement of color or the spontaneous chiral symmetry breaking are encoded in the Greens functions of the theory. In the continuum framework of Dyson-Schwinger equations it is possible to study the infrared re-gime which incorporates these phenomena. Present Dyson-Schwinger studies already give a consistent picture of the dynamics of pure gauge theory. So far, however, the quark dynamics which vitally determines the properties of matter has been considered only in a limited fashion. The aim of this research project is to in-clude in addition to the quark propagator also the quark- gluon vertex into a self-consistent solu-tion scheme in order to study the groundstate and the microscopic degrees of freedom of the theory. Such an improved understanding of the quark interaction is crucial for a consistent de- scription of hadrons as bound states of quarks and gluons. Moreover, this could provide a clear signal for quark confinement by explicit positivity violations in the low energy behavior of the quark propagator. The analysis shall eventually be extended to a finite baryon chemical potential in order to study quark matter at high densities. Due to the absence of other non-perturbative methods, this analysis would provide first quantitative results for the superconducting groundstate at realistic densities. Such a microscopic treatment is very desirable since present model-based results prove to be very sensitive to the uncontrolled model assumptions. Quark matter is of current in-terest, since it could actually be realized in neutron stars due to the high densities in their core. The results of the research project would aid to either detect or rule out the existence of quark matter in neutron stars by means of astrophysical observations.