The Dyson equations for the two-particle Green function and the bound state problem

A new Dyson-like equation for the kernel of the Bethe–Salpeter equation is deduced. Such a representation for the kernel permits to perform partial summation of irreducible diagrams, which is necessary in the presence of bound states in quantum electrodynamics. There by the calculation of the energy shifts in hydrogenic atoms is considerably simplied.
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