Parity of the neutron consistent with neutron-antineutron oscillations

In the analysis of neutron-antineutron oscillations, it has been recently argued in the literature that the use of the $igamma^{0}$ parity $n^{p}(t,-vec{x})=igamma^{0}n(t,-vec{x})$ which is consistent with the Majorana condition is mandatory and that the ordinary parity transformation of the neutron field $n^{p}(t,-vec{x}) = gamma^{0}n(t,-vec{x})$ has a difficulty. We show that a careful treatment of the ordinary parity transformation of the neutron works in the analysis of neutron-antineutron oscillations. Technically, the CP symmetry in the mass diagonalization procedure is important and the two parity transformations, $igamma^{0}$ parity and $gamma^{0}$ parity, are compensated for by the Pauli-Gursey transformation. Our analysis shows that either choice of the parity gives the correct results of neutron-antineutron oscillations if carefully treated.