A new matrix representation of the Maxwell equations based on the Riemann-Silberstein-Weber vector for a linear inhomogeneous medium

Abstract

An eight dimensional matrix representation of the Maxwell equations for a linear inhomogeneous medium has been obtained earlier based on the Riemann-Silberstein-Weber vector starting from the equations satisfied by it. A new eight dimensional matrix representation, related to the ealier one by a similarity transformation, is derived starting ab initio from the Maxwell equations. The new representation has a more advantageous structure compared to the earlier one from the point of view of applications. In the case of a homogeneous medium the new matrix representation reduces to a block diagonal form with four two dimensional Pauli matrix blocks along the diagonal. This matrix representation of the Maxwell equations should be suitable for studying the propagation of electromagnetic waves in a linear inhomogeneous medium, particularly adopting techniques used for studying time evolution equations in quantum mechanics.

Qubit Lattice Algorithms Based on the Schrödinger-Dirac Representation of Maxwell Equations and Their Extensions

“…There has been much interest in rewriting the Maxwell equations in operator form and exploit their similarity to the Schrodinger-Dirac equation from the early 1930s (e.g., see the references in [19]). For homogeneous media, the qubit representation of the electric and magnetic fields, E, H, leads to a Dirac equation in a fully unitary representation.…”