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 four-dimensional 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 label $H_h$ grade the sixteen generators $\tau_\mu\otimes\sigma_\nu$, organizing the $\Delta L=2$ sector. This grading resolves a common ambiguity: helicity-preserving directions $\tau_{1,2}\otimes\sigma_{0,3}$ carry pseudo-Dirac propagation, with coefficient $\kappa_{\rm pD}=\Delta m^2/(4E)$ and active--sterile conversion, whereas helicity-flipping directions $\tau_{1,2}\otimes\sigma_{1,2}$ carry Majorana mass insertions, neutrinoless-double-beta effective mass factors, and active--active neutrino--antineutrino coherence. We derive the one-particle Majorana projection from the field-level condition, clarify the phase convention, and separate the Lagrangian mass insertion from the induced propagation Hamiltonian. The construction classifies the kinematical channels activated by Majorana masses, pseudo-Dirac splittings, medium-induced spin coherence, or other $\Delta L=2$ dynamics; it does not assume that neutrinos are Majorana particles.