On the integral representation of electromagnetic field vectors

Integral representations of the electromagnetic field vectors are derived by the systematic use of a free-space Green's function and file appropriate Green's theorem. The resulting integrals are in terms of the tangential components of the field vectors at the boundary surface. These representations satisfy Maxwell's equations even for open surfaces, thus additional Kottler's boundary-line charges are not required. Several alternative representations are derived and related to previously known formulas. Some of the computational aspects of these alternatives are pointed out.