Equivalent Waveguide Representation for Dirac Plane Waves

Abstract

Ideas about the electron as a sort of a bound electromagnetic wave and/or the electron as electromagnetic field trapped in a (equivalent) waveguide can be found more or less explicitly in many papers. What we want to show here is that the Dirac equation for electron and positron plane waves admits an equivalent electrical circuit, consisting of an equivalent transmission line. The same transmission line is representative of a mode in waveguide, so one can also say that the Dirac equation for plane waves includes an implicit representation in terms of an equivalent waveguide. All calculations will be carried out in elementary form with the usual notations of circuit theory and electromagnetism and without the need to resort to Clifford algebra as in previous papers.