====== TTP99-40 CPT-invariant two-fermion Dirac equation with extended hyperfine operator ====== For the S-states of muonium and positronium, the hyperfine shifts to the order $\alpha^6$ of a recently derived two-fermion equation with explicit $\cal CPT$-invariance are checked against the results of a nonrelativistic reduction, and the leading $\alpha^8$ shifts are calculated. An additional hyperfine operator is discovered which can milden the singularity for $r\to 0$ of the Dirac hyperfine operator, such that the resulting extended operator can be used nonperturbatively. The binding correction to magnetic moments is mentioned. |**V. Hund and H. Pilkuhn** | |** J. Phys. B33 1617 2000 ** | | {{preprints:1999:ttp99-40.pdf|PDF}} {{preprints:1999:ttp99-40.ps|PostScript}} [[http://arxiv.org/abs/hep-ph/9910281|arXiv]] | | |