We analyze the T-invariance violation in probabilities of flavor transitions and neutrino spin rotation in a dense medium in an electromagnetic field. Since the electromagnetic field and the potentials of interaction with the medium appear in the wave equation for the neutrino, the model considered here is a theory with Lorentz-invariance violation. For such models, the conditions for the CPT theorem are not satisfied, and T-invariance violation is not necessarily a consequence of CP invariance violation. We have obtained the sufficient condition for T-invariance violation, which implies that T-symmetry can be violated not only because of the presence of a CP-violating phase in the mixing matrix, but also due to simultaneous influence of the medium and the electromagnetic field. We have obtained the probabilities of spin-flavor transitions of the neutrino in the three-flavor model with account for neutrino diagonal magnetic moments and the interaction with the medium only via neutral currents. Studying the explicit form of the probabilities, we conclude that the transition probabilities for right-handed antineutrinos in a medium consisting of antiparticles differ from the transition probabilities for left-handed neutrinos in a medium of particles only in the sign of the T-violating term.
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