  We present a general method for incorporating an external electromagnetic
field into descriptions of few-body systems whose strong interactions are
described by integral equations. In particular, we address the case where the
integral equations are those of quantum field theory and effectively sum up an
infinite number of Feynman diagrams. The method involves the idea of gauging
the integral equations themselves, and results in electromagnetic amplitudes
where an external photon is effectively coupled to every part of every strong
interaction diagram in the model. Current conservation is therefore implemented
in the way prescribed by quantum field theory. We apply our gauging procedure
to the four-dimensional integral equations describing a system of three
distinguishable relativistic particles. In this way we obtain the expressions
needed to calculate all possible electromagnetic processes of the three-body
system. An interesting aspect of our results is the natural appearance of a
subtraction term needed to avoid the overcounting of diagrams.
