A non-relativistic wave equation of second order in time II, electromagnetic interaction

In this paper it is shown that the electromagnetic interaction can be introduced according to the usual prescription of the minimal electromagnetic interaction into a field equation of second order in time and of fourth order in the space coordinates for bosons, which was proposed in a previous paper. We derive the interaction Hamiltonian for the non-relativistic boson field and the electromagnetic field, as well as the Feynman rules, which have to be used in a perturbation expansion. We have obtained in this way a non-relativistic theory of bosons with electromagnetic interaction in which pair formation or annihilation of the bosons may occur. We calculated some characteristic examples of cross sections and could show that the cross sections provide a non-relativistic limit of the results of the relativistic theory.