under consideration. We find in the infrared limit the functions Λ$_{1}$$_{,}$$_{2}$$_{,}$$_{3}$$_{,}$$_{4}$, on which the three polarization operator eigenvalues and eigenvectors depend in an irrational way, in terms of the field derivatives of the effective action functional defined on constant background field to see explicitly that the eigenvalues disappear in the zero point of the excitation 4-momentum as a consequence of gauge invariance. In Section III this property is used to ground the statement that there always exist mass- less excitations to be identified with photons present in two polarization modes, whereas any number of massive branches may be present in all the three modes. The corresponding excitations have the same quantum numbers as photons and supply poles to the same prop- agator. To avoid a possible misunderstanding it is worth stressing that we do not keep to the definition of the photon mass as its 4-momentum squared k 2 = 0, used by some authors. In our opinion, such word usage is counterproductive, because, if followed, it would make us recognize a photon in a standard isotropic medium with a constant refraction index as massive. This would make the notion of the photon mass indiscriminate. On the contrary, for us, the mass of an excitation is its rest energy, i.e. the value of its frequency (energy) when its spatial momentum is zero. Then, the excitations, whose dispersion curves include the origin in the momentum space, are referred to as photons. By restricting the group velocity of an excitation below the speed of light we establish that in the special frame each dispersion curve is limited from above in the plane ( √ k 2 0 − k 2 $_{3}$, | k$_{⊥}$ | ) by a straight line that crosses the dispersion curve at | k$_{⊥}$ | = 0 and is inclined to the coordinate axes at the angle of 45 o (see Fig.1). Massless branches are restricted to the exterior of the light cone √ k 2 0 − k 2 3 ≤ | k$_{⊥}$ | , whereas massive ones may cross it. This situation is similar to the magnetic field alone [3], because the general field also specializes only one direction in the space, namely the common direction of the magnetic and electric fields in the special reference frame. In Section IV we describe, in the special frame, polarizations of electric and magnetic fields of the eigenmodes and find, specially, that the electric fields of modes 2 and 3, which are responsible for massless excitations, lie in a common plane spanned by two 3-vectors, one of which is orthogonal to the plane, where the external fields and the propagation momentum k lie, while the other belongs to that plane and makes a universal angle that depends only on momentum components with the external fields. Electric field of mode 1 is polarized along k$_{⊥}$ . In the same section we find the large-distance behavior of the magnetic field produced 7