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We present a parity-doublet theorem for the representation of the intrinsic parity of Majorana fermions, which is expected to be useful also in condensed matter physics, and it is illustrated to provide a criterion of neutron-antineutron oscillation in a BCS-like effective theory with $\Delta B=2$ baryon number violating terms.
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We assume that the free Majorana particles in Minkowski space respect the full Lorentz symmetry, including P and T and thus C, due to CPT
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R.N. Mohapatra, J. Phys. G: Nucl. Part. Phys. 36
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