Renormalization of the energies stored around a Wiener–Hopf structure: I

Abstract

A programme of renormalization of the electromagnetic energy stored around a structure admitting a solution through the Wiener–Hopf technique is proposed. The infinites of the stored magnetic energy also appear in the stored electric energy and they are suppressed freely. There are divergencies due to spatial integrations that prove to be completely renormalizable. Moreover the Wiener–Hopf procedure for the solution of the radiation from the semi-infinite parallel-plate duct gives rise to two other kinds of divergencies. First, the form of the spectrum eigenfunction causes a contribution to the stored energies from the wave-number visible region where the eigenfunction is "peaked" at certain points. Second, the squared spectrum eigenfunctions have a nonsummable singularity at the lower boundary of the visible region. The renormalizability of the formulae of the energies in both of these cases is proved.