Chiral measurements in quenched lattice QCD with Fixed Point fermions

We construct a parametrization of a Fixed Point (FP) Dirac operator and apply it in quenched lattice QCD. The symmetry requirements for a general lattice Dirac operator are discussed and an efficient way to make a practical construction of general lattice Dirac operators is provided. We use such a lattice Dirac operator to approximately solve the Renormalization Group equation that defines the FP Dirac operator in an iterative procedure. We discuss the properties of this parametrization and show that its breaking of chiral symmetry and its scaling violations in hadron specroscopy are much reduced compared to the Wilson Dirac operator. Furthermore, we discuss the overlap construction with the parametrized FP Dirac operator and its properties. Using the Atiyah-Singer index theorem, a consequence of chiral symmetry, we calculate the quenched topological susceptibility. Finally, we determine the renormalized low-energy constant Sigma of quenched Chiral Perturbation Theory using a finite volume scaling technique.