On the Nonuniqueness of Equivalent Current Sheets Supporting Discontinuous Electromagnetic Fields

In this work, it is shown that the familiar boundary conditions across an interface are not unique. They can be reformulated in a number of alternative ways without affecting the solution outside the interface. Surface electric and magnetic current distributions used to compensate for the discontinuities in electric and magnetic tangential fields are interchangeable, leading to a variety of boundary conditions. In particular, the introduction of a magnetic surface current is not necessary to account for a discontinuity in the transversal electric field because it can be exchanged for a highly singular electric current, causing no difference in the solution except within the source region. Examples for conducting electric and magnetic sheets are given.