Relativistic corrections to the Zeeman splitting of hyperfine structure levels in two-fermion bound-state systems

A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is presented. The approach is based on the variational equation for bound states derived from quantum electrodynamics [1]. Relativistic corrections to the g-factor are obtained up to O(alpha^2). Calculations are provided for all quantum states and for arbitrary fermionic mass ratio. In the one-body limit our calculations reproduce the formula for the g-factor (to O((Z*alpha)^2)) obtained from the Dirac equation. The results will be useful for comparison with high-precision measurements.