Previously, we presented an alternative relativistic formalism for nonrelativistic two-body bound-state systems [T. Zhang, L. Xiao, and R. Koniuk, Can. J. Phys. 70, 670 (1992)]. The kernel of the integral equation for the bound-state systems is generated by summing Feynman scattering amplitudes and multiplying by a bound-state amplitude. In this paper, we present our calculations of two-loop contributions to hyperfine splitting of positronium to order ${\mathrm{\alpha }}^6$ coming from vacuum-polarization corrections to two-exchange-photon interactions.

• Received 25 October 1993

DOI:https://doi.org/10.1103/PhysRevA.49.2411