calCcalPcalT-invariant two-fermion Dirac equation with extended hyperfine operator

For the S-states of muonium and positronium, the hyperfine shifts to the order 6 of a recently derived two-fermion equation with explicit -invariance are checked against the results of a nonrelativistic reduction, and the leading 8 shifts are calculated. An additional hyperfine operator is discovered which can milden the singularity for r 0 of the Dirac hyperfine operator, such that the resulting extended operator may be used nonperturbatively. A binding correction to magnetic moments is derived from -invariance.