True muonium on the light front

The muon problem of flavor physics presents a rich opportunity to study beyond standard model physics. The as yet undiscovered bound state (μ+μ-), called true muonium, presents a unique opportunity to investigate the muon problem. The near-future experimental searches for true muonium will produce it relativistically, preventing the easy application of non-relativistic quantum mechanics. In this thesis, quantum field theory methods based on light-front quantization are used to solve an effective Hamiltonian for true muonium in the Fock space of |μ+μ-> , |μ+μ-γ> , |e+e->, |e+e-γ>, |τ+τ-> , and |τ+τ-γ> . To facilitate these calculations a new parallel code, True Muonium Solver With Front-Form Techniques (TMSWIFT), has been developed. Using this code, numerical results for the wave functions, energy levels, and decay constants of true muonium have been obtained for a range of coupling constants α. Work is also presented for deriving the effective interaction arising from the |γγ sector’s inclusion into the model.