Quantum Chromodynamics with Chiral Quarks

Quantum-Chromodynamics (QCD) is the theory of quarks, gluons and their interaction. It has an important almost exact symmetry, the so-called chiral symmetry (which is actually broken spontaneously). This symmetry plays a major role in all low-energy hadronic processes. For traditional formulations of lattice QCD, CPU-time and memory limitations prevent simulations with light quarks and this symmetry is seriously violated. During the last years successful implementations of the chiral symmetry for lattice QCD have been constructed. We use two approximate implementations (both of them in the quenched approximation) with different specific advantages. We have also made progress towards the development of a practical algorithm to allow for simulations with dynamical quarks. In 2003 a series of discoveries of a new class of particles, called pentaquarks, has created very strong interest in lattice studies of resonance states. We have performed such studies with a specific method for the N* resonances with very satisfying results and are currently working on similar calculations for the pentaquarks. We have also addressed the question, which type of gauge field configurations is responsible for confinement and chiral symmetry breaking. Finally we are calculating three-point functions. We hope that for the small quark masses which we reach the results will not only be of direct phenomenological interest, but will also test predictions from chiral perturbation theory.