Allowance for the effects of bound states in positronium

To take into account the effects of bound states of particles in quantum electrodynamics it is suggested that the Coulomb Green's function should be used at all stages in the construction of the quasipotential. For the first time in the quasipotential approach, the contribution to the hyperfine splitting of the positronium ground state due to the singlephoton direct diagram of second order is considered to accuracy $\alpha^6\ln\alpha$.