Eichtheorien mit einem Flavour dynamischer Fermionen

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In this project gauge theories with a single flavour of dynamical fermions are investigated. This includes Quantum Chromodynamics (QCD) with one quark flavour and supersymmetric Yang-Mills theory with a gluino. The numerical treatment of a single fermion flavour is essentially different from the treatment of a doublet with degenerate masses. In particular the quark determinant of a single fermion flavour can become negative. It is expected that at vanishing quark mass a singularity occurs and at negative quark masses the CP symmetry of the groundstate is broken spontaneously. In our project we investigate the properties of QCD with one flavour and its relation to supersymmetric Yang-Mills theory numerically. This involves the singularity, the sign effect of the fermion determinant and the spectrum of low-lying hadron states.