Properties of quarks and mesons in the Dyson-Schwinger/Bethe-Salpeter approach

Understand

In this thesis, the Dyson-Schwinger - Bethe-Salpeter formalism is investigated and used to study the meson spectrum at zero temperature, as well as the chiral phase transition in finite-temperature QCD.

• First, the application of sophisticated matrix algorithms to the numerical solution of both the homogeneous Bethe-Salpeter equation (BSE) and the inhomogeneous vertex BSE is discussed, and the advantages of these methods are described in detail.
• Turning to the finite temperature formalism, the rainbow-truncated quark Dyson-Schwinger equation is used to investigate the impact of different forms of the effective interaction on the chiral transition temperature.
• A strong model dependence and no overall correlation of the value of the transition temperature to the strength of the interaction is found.