Internal pseudospin, lepton-number superselection, and neutrino--antineutrino coherence in massive neutral-fermion one-particle states

Abstract

At fixed three-momentum, massive Dirac neutrino one-particle states span a 4D space of particle--antiparticle identity and helicity. We show that helicity flip, charge conjugation, and their product close an internal $SU(2)$ pseudospin subalgebra within $SU(4)$, distinct from the Wigner little group. Its helicity generator is the lepton-number-weighted spin rotation $U_1=2LJ_2$. The lepton-number $L$ and helicity $\mathcal H_h$ grade the 16 generators $\tau_\mu\otimes\sigma_\nu$, organizing the $\Delta L=2$ sector. Helicity-preserving directions $\tau_{1,2}\otimes\sigma_{0,3}$ carry the pseudo-Dirac mixing $\kappa_{\rm pD}=\Delta m^2/4E$ (active--sterile), while helicity-flipping directions $\tau_{1,2}\otimes\sigma_{1,2}$ carry the neutrinoless double-beta decay mass factor (active--active). Furthermore, charge conjugation matches the $U_2$ generator. The Majorana condition is thus a projection onto the $U_2=+1$ eigenspace, where only the Wigner algebra survives. This framework algebraically classifies Majorana masses and pseudo-Dirac splittings without assuming neutrinos are Majorana particles.