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

An eight dimensional matrix representation of the Maxwell equations for a linear inhomogeneous medium has been derived earlier based on the Riemann-Silberstein-Weber vector starting from the equations satisfied by it. A new eight dimensional matrix representation, related to the earlier one by a similarity transformation, is deduced starting ab initio from the Maxwell equations. In this process the Riemann-Silberstein-Weber vector is obtained as natural basis for the matrix representation of 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 it reduces to a block diagonal form with four two dimensional Pauli matrix blocks along the diagonal and in the case of a linear inhomogeneous medium it should be suitable for studying the propagation of electromagnetic waves adopting the techniques of quantum mechanics.