Self-energy effect in a relativistic bound state problem

A modification of the Wick-Cutkosky equation for the relativistic bound state of two scalar particles interacting through the exchange of a massless scalar field within the ladder approximation has been considered by incorporating the self-energy diagrams in the integral kernel. An exact analytical solution of the equation is obtained at vanishing total energy and it is shown that the self-energy effects generally diminish the eigenvalues in agreement with the findings of Liet al, who, however solved the equation numerically for the case of massive scalar exchange. An additional feature of the modified equation is that it preserves the 0(5) symmetry at zero total energy as was first noted by Cutkosky for the scalar bound state equation without self-energy effects.