We consider the Maxwell equations in a domain with Lipschitz
boundary and the boundary integral operator A occuring in the Calder?n
projector. We prove an inf-sup condition for A using a Hodge decomposition.
We apply this to two types of boundary value problems: the exterior scattering
problem by a perfectly conducting body, and the dielectric problem with two
different materials in the interior and exterior domain. In both cases we
obtain an equivalent boundary equation which has a unique solution. We then
consider Galerkin discretizations with Raviart-Thomas spaces. We show that
these spaces have discrete Hodge decompositions which are in some sense close
to the continuous Hodge decomposition. This property allows us to prove
quasioptimal convergence of the resulting boundary element methods
