  Instead of using local field equations - like the Dirac equation for spin-1/2
and the Klein-Gordon equation for spin-0 particles - one could try to use
non-local field equations in order to describe scattering processes. The latter
equations can be obtained by means of the relativistic energy together with the
correspondence principle, resulting in equations with a square root operator.
By coupling them to an electromagnetic field and expanding the square root (and
taking into account terms of quadratic order in the electromagnetic coupling
constant e), it is possible to calculate scattering matrix elements within the
framework of quantum electrodynamics, e.g. like those for Compton scattering or
for the scattering of two identical particles. This will be done here for the
scalar case. These results are then compared with the corresponding ones based
on the Klein-Gordon equation. A proposal of how to transfer these reflections
to the spin-1/2 case is also presented.
