electric component in any Lorentz frame was damped by the fact that within the pertur- bation theory such field is, according to Schwinger [9], unstable with regard to spontaneous electron-positron pair production. (It is seen from [10] that the imaginary part of the effec- tive Lagrangian on constant fields calculated within one- and two-loop accuracy is nonzero if either F < 0 , G = 0 or F ≶ 0 , G = 0). A special theory for handling such fields was developed in [11]. After exploited in one-loop calculations of the polarization operator in [12] it indicated, with the help of the general analysis in [13], that C-invariance (the Furry theorem) is violated, while PT-invariance (the Onsager theorem) is preserved, hence there is no CPT. Actually, a matrix (namely, Ψ (5) µν in [12], [13]) appears in the decomposition of the one-loop polarization operator, which is odd in the external field and hence incompatible with the C-invariance, but compatible with the Onsager theorem (see Refs. [13],[5] for its formulation fit for the present use), because it is antisymmetric with respect to the indices. On the other hand, the matrix Ψ (7) $_{µν}$, also odd in the external field, but symmetric under the permutation of its indices, that might contradict also the Onsager theorem, is not involved. Once the external field instability that contradicts CPT-invariance and is itself a violation of general principles depends on the perturbation theory and is unknown beyond it, it is ignored in the analysis of the present paper based exclusively on these principles. During the years that followed most efforts were devoted to important special case of one-invariant field with G = 0 and F ≥ 0 that corresponds to a purely magnetic field in a special Lorentz frame. We shall refer to it as ”magnetic-like”. The general analysis of Ref. [4] is also valid in this case, whereas the corresponding one-loop polarization operator is contained in the formulae of that work as a simple limit G = 0 , analyzed specifically a bit later in [14]. This limiting polarization operator was recalculated separately by Tsai [15]. It must be pointed that the one-loop polarization operator in a magnetic-like field for vanishing virtuality, k 2 = 0, had been known earlier, after the important papers by Adler et al. [16]. The simplification k 2 = 0 is sufficient for considering small dispersion and has been permanently playing a significant role in astrophysical applications. It does not serve, however, the case when large deviations from the vacuum dispersion law take place, as is the case when cyclotron resonances of the vacuum polarization at the thresholds of creations of free [14] or mutually bound [17] - [19] electron-positron pairs are exploited to produce the photon capture [20] by a strong magnetic field of pulsars. Besides, the assumption that k 2 = 0 completely excludes massive states and, moreover, the whole of the one of the three 4