Rotation in electromagnetic field equations: a discussion, interpretation and application

Rotation matrices are shown to be present is several types of electromagnetic field analysis. These include the duality transform, transmission line analysis and path integral scattering analysis. The rotation matrix is shown to be the Fourier transform of the propagator. It is then shown that a simple transmission line numerical expression useful for analyzing inhomogeneous transmission lines in the time domain arises by taking the Fourier transform of the transmission line ABCD matrix and convolving with the present time voltage and current.