Quark Propagator Studies with Overlap Fermions in Lattice QCD

Lattice QCD is the only first-principles approach to performing calculations in the nonperturbative regime of QCD. Within this paradigm, continuum QCD is discretised and embedded into a finite-volume lattice of Euclidean spacetime points. This process is nontrivial, particularly in the fermion sector. The overlap formalism provides an implementation of fermions on the lattice which incorporates chiral symmetry. Although this is desirable, it comes at great computational expense, restricting the use of overlap fermions to situations where their favourable properties are deemed beneficial or necessary. We make extensive use of overlap fermions in this work. We consider the Landau-gauge overlap quark propagator from dynamical gauge fields for the first time, where the overlap formalism provides a straightforward, prescribed way of extracting the mass and renormalisation functions. Furthermore, the chiral nature and sensitivity to gauge field topology of the overlap operator makes the overlap quark propagator the ideal probe to study the role of centre vortices in dynamical chiral symmetry breaking. To this end, we investigate the effect of centre-vortex modification of QCD ground-state fields on the quark propagator. In order to compute vortex-only quark propagator we perform an extensive investigation into the viability of various smoothing algorithms applied to vortex-only gauge fields, developing novel approaches necessary to satisfy the smoothness condition of the overlap Dirac operator. Given recent suggestions that chiral symmetry could be key to understanding the origin of the low-lying nature of the Roper resonance, we also systematically examine the role of chiral symmetry in the nucleon spectrum by directly comparing the Wilson clover and overlap fermion actions.Thesis (Ph.D.) -- University of Adelaide, School of Physics, Chemistry and Earth Sciences, 202