| This document consists of three chapters. The first chapter includes a detailed description of neutrino oscillations with an emphasis on the naturalness of obtaining a small value Ue3 within the Maki-Nakagawa-Sakata mixing matrix. With the use of the seesaw mechanism, it is found that the upper bound on this particular element is approaching its lower limit when we assume a very natural set of criteria for the origins of leptonic mixing. Also obtained are some general expressions which could provide insight into the Majorana nature of neutrino oscillations.; The second chapter explores the use of operator methods in a 1/ Nc expansion for magnetic moments in QCD. An analysis of the entire set of magnetic moments is provided, including an explicit calculation of all twenty seven corresponding operators. A prediction of the sixteen unknown magnetic moments is also given, which were found using only the Wigner-Eckart theorem and a simple least squares fit to the available data. Using the predicted magnetic moments, we were also able to predict the six radiative decay widths corresponding to the Sigma*+, Sigma *0, xi*0, and xi*-.; In the third chapter; using a formalism established to include systematic corrections to the leading order S-matrix elements, we derive expressions for the pion photoproduction amplitudes in the 1/Nc expansion of QCD, and obtain linear relations directly from this expansion that relate electromagnetic multipole amplitudes at all energies. The leading-order relations in 1/Nc compare favorably with available data, while the next-to-leading order relations seem to provide only a small improvement. However, when resonance parameters are compared directly, the agreement at O(1/Nc) or O(1/ N2c ) is impressive. |
