Majorana neutrino as Bogoliubov quasiparticle

Kazuo Fujikawa,Anca Tureanu

doi:10.1016/j.physletb.2017.09.051

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 CψC†=ψ 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 ψ→exp⁡[iαγ5]ψ 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.

Highlights

Introduction from a chiralWeyl fermion which satisfiesThe Majorana fermions received much attention recently in particle physics in d = 1 + 3 [1,2,3,4] and in condensed matter physics in d = 1 + 3 or less dimensions [5,6,7]
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
It is generally believed that the Majorana fermion and the Weyl fermion are identical in d = 1 + 3 as is seen by writing them in the two-component spinor notation

Summary

Introduction from a chiral Weyl fermion which satisfies

It is generally believed that the Majorana fermion and the Weyl fermion are identical in d = 1 + 3 as is seen by writing them in the two-component spinor notation. It is not obvious at all how a self-conjugate object is identical to a complex chiral object. We discuss some basic properties of Majorana and Weyl fermions using a relativistic analogue of Bogoliubov transformation in d = 1 + 3 space–time. The Majorana neutrino could become the first Bogoliubov quasiparticle observed in particle physics

Bogoliubov transformation

Chiral symmetry and related issues