The process of photon splitting is investigated in the presence of strongly magnetized electronpositron plasma. The amplitude of the process is calculated in the general case of plasma with nonzero chemical potential and temperature. The polarization selection rules and corresponding partial amplitudes for allowed splitting channels are obtained in the case of charge-symmetric plasma. It is found that the new splitting channel forbidden in magnetized vacuum becomes allowed. The absorption rates of the photon splitting are calculated with taking into account the photon dispersion and wave function renormalization. In addition, the comparison of photon splitting and Compton scattering process is made. The influence of the reactions under consideration on the radiation transfer in the framework of the magnet ar model of a soft gamma repeater burst is discussed. PACS numbers: 95.30.Cq, 14.70.Bh, 52.25.Os,13.40.-f * mch@uniyar.ac.ru † rda@uniyar.ac.ru 1 We use natural units c = = k = 1, m is the electron mass, and e > 0 is the elementary charge.2 The details of the calculation of the amplitude can be found in Ref.[31].

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The process of neutrino production of electron positron pairs in a magnetic field of arbitrary strength, where electrons and positrons can be created in the states corresponding to excited Landau levels, is analysed. The mean value of the neutrino energy loss due to the process ν → νe − e + is calculated. The result can be applied for calculating the efficiency of the electron-positron plasma production by neutrinos in the conditions of the Kerr black hole accretion disc considered by experts as the most possible source of a short cosmological gamma burst. The presented research can be also useful for further development of the calculation technic for an analysis of quantum processes in external active medium, and in part in the conditions of moderately strong magnetic field, when taking account of the ground Landau level appears to be insufficient. * 1 We use natural units c = = kB = 1, me is the electron mass, and e is the elementary charge.

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