Retarded functions and potential scattering

Conclusion

We have shown that it is possible to determine the scattering amplitude of an axiomatic non-relativistic field theory model; if the particles involved interact with a fixed source only, provided the equation for the retarded functions is properly restricted by certain boundary conditions. Tn this case, the problem is reduced to the solution of an integral equation of almost Predholm type, which has already long been dealt with in literature.

The application of the similar Omnès method, however, leads to difficulties, which might be overcome by an iteration procedure analogous to that of Ghew and Mandelstam. We do not know the conditions, under which this scheme converges to a unique solution, nor do we know if there is a connection, for instance, between the Born series and the successive steps of the above mentioned iteration method. Apart from this, it seems to us that the application of the Omnès method is not very useful in our case, though it may have its advantages in relativistic field theory.