Relativistic corrections to the fine structure of positronium

The quasipotential method is used to calculate relativistic corrections in the positronium-fine-structure intervals 2(3)S(1)-2(3)P(J). From analysis of one-and two-photon interactions, corrections of order m alpha(6) are found for positronium S states in the second order of perturbation theory. The contribution of the two-photon annihilation diagrams to the interaction operator for P-wave positronium is determined, and corrections of orders alpha(5)R(infinity) and or alpha(5)ln alpha R-infinity to the P-wave levels of positronium are calculated.