Abstract
We discuss the polarization selection rules for splitting of the two principal electromagnetic modes that propagate in a vacuum polarized by a superstrong magnetic field (B>0.1B_{cr} ~ 4x10^{12} G). We show that below the threshold of free pair creation the selection rules found by Adler in the limit of weak dispersion remain unaffected by taking the resonant effects into consideration, i.e., splitting of one mode is strictly forbidden, while splitting of the other is allowed.
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