1. Majorana neutrino as Bogoliubov quasiparticle
- Author
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Kazuo Fujikawa, Anca Tureanu, and Department of Physics
- Subjects
High Energy Physics - Theory ,Nuclear and High Energy Physics ,Sterile neutrino ,Particle physics ,Helical Dirac fermion ,High Energy Physics::Lattice ,FOS: Physical sciences ,114 Physical sciences ,01 natural sciences ,Superconductivity (cond-mat.supr-con) ,symbols.namesake ,High Energy Physics - Phenomenology (hep-ph) ,0103 physical sciences ,OSCILLATIONS ,010306 general physics ,Majorana equation ,Physics ,Condensed Matter::Quantum Gases ,010308 nuclear & particles physics ,Condensed Matter - Superconductivity ,High Energy Physics::Phenomenology ,Fermion ,Physics::History of Physics ,lcsh:QC1-999 ,High Energy Physics - Phenomenology ,Bogoliubov transformation ,MAJORANA ,Dirac fermion ,High Energy Physics - Theory (hep-th) ,symbols ,lcsh:Physics ,Majorana fermion - 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 ${\cal C}\psi{\cal C}^{\dagger}=\psi$ 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 $\psi\rightarrow \exp[i\alpha\gamma_{5}]\psi$ 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., Comment: 15 pages; correction of the formula after eq. (6), in the version published in Phys. Lett. B
- Published
- 2017