A Covariant Gauge-Invariant Three-Dimensional Description of Relativistic Bound States

A formalism is presented that 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.