Electromagnetic mass shifts in non-Lagrangian field theory

The electromagnetic interactions of hadrons are considered in a model in which both the hadrons and the photons are spinless. The perturbation theory of this model is developed in a way which takes the strong interactions rigorously into account. An expression for the second-order electromagnetic mass shifts of the hadrons is derived. The customary formula expressing these mass shifts as integrals over the Compton scattering amplitude is shown to be inaccurate. The correct expression differs from the old one by a changed integration contour. In favourable cases the two expressions coincide if the integrations over the four components of the photon momentum are carried out in a certain order. This order of integration must in general not be changed.