We analyze status of C, P and T discrete symmetries in application to neutron-antineutron transitions breaking conservation of baryon charge ℬ by two units. At the level of free particles, all these symmetries are preserved. This includes P reflection in spite of the opposite internal parities usually ascribed to neutron and antineutron. Explanation, which goes back to the 1937 papers by Majorana and Racah, is based on a definition of parity satisfying P2 = -1, instead of P2 = 1, and ascribing P = i to both, neutron and antineutron. We apply this to C, P and T classification of six-quark operators with |Δℬ| = 2. It allows to specify operators contributing to neutron-antineutron oscillations. Remaining operators contribute to other |Δℬ| = 2 processes and, in particular, to nuclei instability. We also show that presence of external magnetic field does not induce any new operator mixing the neutron and antineutron provided that rotational invariance is not broken.
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We thank Martin Einhorn, Susan Gardner, Yuri Kamyshkov, Kirill Melnikov, Rabi Mohapatra, Adam Ritz and Misha Voloshin for helpful discussions. A. Vainshtein appreciates hospitality of the Kavli Institute for Theoretical Physics where his research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958.