Thesis (Ph. D.) in Physics--University of Maine, 2003. / Includes vita. Includes bibliographical references (leaves 99-103).

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A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, December 2014. / In this thesis the evolution equations of the Yukawa couplings and quark flavour mixings are derived for the one-loop renormalisation group equations in five and six-dimensional models, compactified in different possible ways to yield standard four space-time dimensions. Different possibilities for the matter fields are discussed, such as the case of bulk propagating or brane localized fields. We discuss in both cases the evolution of the Yukawa couplings, the Jarlskog parameter and the Cabibbo-Kobayashi-Maskawa matrix elements, finding that for both scenarios, as we run up to the unification scale, significant renormalisation group corrections are present. We also discuss the results of different observables of the five-dimensional universal extra dimension model in comparison with those of six-dimensional models and the model dependence of the results. We also studied the scaling of the mass ratios and the implications for the mixing angles in these six-dimensional model as well as the 5D Minimal Supersymmetric Standard Model on an S1/Z2 orbifold. The renormalisation group equation evolutions for the Higgs sector and for the neutrino sector in six-dimensional models are also investigated. The recent experimental results of the Higgs boson from the LHC allow, in some scenarios, stronger constraints on the cutoff scale to be placed, from the requirement of the stability of the Higgs potential.

A renormalization analysis is presented for a generalized Harper equation (1 + α cos(2π(ω(i + 1/2) + φ)))ψi+1 + (1 + α cos(2π(ω(i − 1/2) + φ)))ψi−1 +2λ cos(2π(iω + φ))ψi = Eψi. (0.1) For values of the parameter ω having periodic continued-fraction expansion, we construct the periodic orbits of the renormalization strange sets in function space that govern the wave function fluctuations of the solutions of the generalized Harper equation in the strong-coupling limit λ→∞. For values of ω with non-periodic continued fraction expansions, we make some conjectures based on work of Mestel and Osbaldestin on the likely structure of the renormalization strange set.

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Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Physics. / Vita. / Includes bibliographical references. / by Jeffrey F. Nicoll. / Ph.D.

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