Topics in quantum chromodynamics: two loop Feynman gauge calculation of the meson nonsinglet evolution potential and fourier acceleration of the calculation of the fermion propagator in lattice QCD

Part I of this thesis is a perturbative QCD calculation to two loops of the meson nonsinglet evolution potential in the Feynman gauge. The evolution potential describes the momentum dependence of the distribution amplitude. This amplitude is needed for the calculation to beyond leading order of exclusive amplitudes and form factors. Techniques are presented that greatly simplify the calculation. The results agree with an independent light-cone gauge calculation and disagree with predictions made using conformal symmetry. In Part II the author presents a Fourier acceleration method that is effective in accelerating the computation of the fermion propagator in lattice QCD. The conventional computation suffers from critical slowing down: the long distance structure converges much slower than the short distance structure. by evaluating the fermion propagator in momentum space using fast Fourier transforms, it is possible to make different length scales converge at a more equal rate. From numerical experiments made on a 84 lattice, the author obtained savings of a factor of 3 to 4 by using Fourier acceleration. He also discusses the important of gauge fixing when using Fourier acceleration