  A formalism is presented which allows covariant three-dimensional bound-state
equations to be derived systematically from four-dimensional ones without the
use of delta-functions. The amplitude for the interaction of a bound state
described by these equations with an electromagnetic probe is constructed. This
amplitude is shown to be gauge invariant if the formalism is truncated at the
same coupling-constant order in both the interaction kernel of the integral
equation and the electromagnetic current operator.
