We review the three neutrino problems - the solar neutrino, atmospheric neutrino and the LSND results - and their solutions in terms of neutrino oscillations. We try to explain all three results without introducing a light sterile neutrino. This leads us to consider the possibility that the LSND result is explained by new neutrino interactions. We examine how this New Physics (NP) can influence the solutions of the solar and the atmospheric neutrino problem. We show that only the MSW effect is sensitive to NP neutrino interactions and work out the formalism of how the resonant conversion has to be described in the presence of flavor changing scattering off the electrons in the sun. We study the analytic behavior of the survival probability and carry out a numerical simulation with the modified equations for NP, in order to investigate the changes to the allowed regions in the MSW-plane. Our result is that, depending on the ratio of the NP reaction strength relevant to the MSW-effect to that required for explaining LSND, the small-angle allowed region may disappear or become larger. For some value of this ratio there exists a solution to the solar neutrino problem without mixing. In order to investigate how realistic is the assumption of similar NP couplings for the leptonic reactions relevant to LSND and the MSW-effect, we study the relation of those reactions and the forbidden decay mu --> 3e for two specific extensions of the SM that allow neutrino masses and give L-violating neutrino interactions. We discuss what consequences arise in the left-right symmetric model and the minimal supersymmetric model with broken R-parity. In both models we come to the conclusion that the bound on mu --> 3e rules out a significant change to the MSW-solution, and that the LSND result can be explained naturally with new interactions, provided we assume an additional symmetry that suppresses mu --> 3e (and the new effects to the MSW-solution) sufficiently.

The postscript of the entire thesis can be found here (4.4 Mb).