Simulations of Lattice Fermions with Chiral Symmetry in Quantum Chromodynamics

This thesis is dedicated to explore the feasibility of numerical calculations in the $\epsilon$--regime of QCD for the extraction of physical information. We apply two formulations of the Ginsparg-Wilson fermions the Neuberger operator and the hypercube overlap operator to compute the observables of interest. As a main result we present the comparison of the distributions of the leading individual eigenvalues of the Neuberger operator in QCD and the analytical predictions of chiral random matrix theory. We observe a good agreement as long as each side of the physical volume exceeds about L\approx 1.12\fm. It turns out that this bound for $L$ is generic and sets the size of the physical volume where the axial correlator behaves according to chiral perturbation theory. This allows us to compute a value for the pion decay constant $F_{\pi}$. As an alternative procedure we only consider the contribution from the zero modes. Here we are able to obtain an estimate for $F_{\pi}$ and $\alpha$. As a theoretical development the L\"uscher topology conserving gauge action is investigated. This enables us to sample the observables of interest in the $\epsilon$--regime without recomputing the index. We can report that a promising gauge action has been identified.Comment: Ph.D. thesi

Meson correlation functions at high temperatures

We present preliminary results for the correlation- and spectral functions of different meson channels on the lattice. The main focus lies on gaining control over cut-off as well as on the finite-volume effects. Extrapolations of screening masses above the deconfining temperature are guided by the result of the free ($T=\infty$) case on the lattice and in the continuum. We study the quenched non-perturbatively improved Wilson-clover fermion as well as the hypercube fermion action which might show less cut-off effects.Comment: 6 pages, 8 figures (minor changes, citations added

Lattice Gauge Actions for Fixed Topology

We test a set of lattice gauge actions for QCD that suppress small plaquette values and in this way also suppress transitions between topological sectors. This is well suited for simulations in the epsilon-regime and it is expected to help in numerical simulations with dynamical quarks.Comment: 3 pages. Talk presented at Quark Confinement and the Hadron Spectrum VI, Villasimius, Sardinia, Italy, September 21-25, 2004. References adde

Meson Correlation Functions in the epsilon-Regime

We present a numerical pilot study of the meson correlation functions in the epsilon-regime of chiral perturbation theory. Based on simulations with overlap fermions we measured the axial and pseudo-scalar correlation functions, and we discuss the implications for the leading low energy constants in the chiral Lagrangian.Comment: 3 pages, 3 figures, talk presented at Lattice2003(chiral