NRQED Approach to the Hyperfine Structure of the Muonium Ground State
  The method of NRQED is an adaptation of QED to bound systems. While it is fully equivalent to QED, it enables us to explore the QED bound states systematically as an expansion in the fine structure constant $\alpha$ and velocity ($\sim Z\alpha$) of the bound electron. I describe how to construct the NRQED Hamiltonian choosing recent works on the $\alpha (Z\alpha)$, $\alpha^2 (Z\alpha)$,$\alpha (Z\alpha)^2$, $\alpha (Z\alpha)^3$, and $\alpha^2 (Z\alpha)^2$ radiative corrections to the hyperfine structure of the muonium ground state as examples. 
T. Kinoshita