Introduction to muonium-antimuonium oscillation -- Muonium-antimuonium oscillation in a modified Standard Model -- Supersymmetry and the Minimal Supersymmetric Standard Model -- The muonium-antimuonium oscillation in the extended Minimal Supersymmetric Standard Model -- The constraints from the muon and electron anomalous magnetic moment experiments -- Conclusions.

The muonium-antimuonium oscillation process has been studied for decades both experimentally and theoretically. Of particular interest is that such a muonium-antimuonium oscillation is totally forbidden within the Standard Model because the process violates the individual electron and muon number conservation laws by two units. Hence, its observation will be a clear signal of physics beyond the Standard Model. This thesis involves the computation of the muonium-antimuonium oscillation time scale in a variety of Standard Model extensions. First, the gauge independence of the various 1-loop contributions to this process is demonstrated in the Standard Model modified only with the inclusion of right-handed neutrinos which were used to generate light neutrino masses via the see-saw mechanism. Next the muonium-antimuonium oscillation time scale in a supersymmetric (SUSY) extension of the Standard Model is calculated. The lower bound on the ratio of the two Higgs field VEVs is also discussed by using experimental results. This Doctoral Thesis has been accepted by Purdue University, West Lafayette, USA.