Operator for describing polarization states of a photon in terms of Riemann-Silberstein quantized electromagnetic vector
Based on the quantized electromagnetic described by the Riemann-Silberstein complex vector F, we construct the eigenvector set of F, which makes up an orthonormal and complete representation. In terms of F we then introduce a new operator which can describe the relative ratio of the left-handed and right-handed polarization states of a polarized photon. In F’s eigenvector basis the operator manifestly exhibits a behaviour which is similar to a phase difference between two orientations of polarization of a light beam in classical optics.