Majorana Neutrino as Bogoliubov Quasiparticle

Abstract

We suggest that the Majorana neutrino should be regarded as a Bogoliubov quasiparticle that is consistently understood only by use of a relativistic analogue of the Bogoliubov transformation. The unitary charge conjugation condition $\mathcal{C}\psi {\mathcal{C}}^{†}=\psi$ is not maintained in the definition of a quantum Majorana fermion from a Weyl fermion. This is remedied by the Bogoliubov transformation accompanying a redefinition of the charge conjugation properties of vacuum, such that a C-noninvariant fermion number violating term (condensate) is converted to a Dirac mass. We also comment on the chiral symmetry of a Majorana fermion; a massless Majorana fermion is invariant under a global chiral transformation $\psi \to \exp [i\alpha {\gamma }_5]\psi$ and different Majorana fermions are distinguished by different chiral $U(1)$ charge assignments. The reversed process, namely, the definition of a Weyl fermion from a well-defined massless Majorana fermion is also briefly discussed.

arXiv comment15 pages; correction of the formula after eq. (6), in the version published in Phys. Lett. B

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• Current Density of Majorana Bound States
• Emergence of a new symmetry class for Bogoliubov-de Gennes (BdG) Hamiltonians: Expanding ten-fold symmetry classes
• Seesaw, coherence and neutrino oscillations