Majorana Neutrino as Bogoliubov Quasiparticle

TL;DR

This paper proposes viewing the Majorana neutrino as a Bogoliubov quasiparticle, using a relativistic Bogoliubov transformation to clarify its charge conjugation and mass properties, and discusses its chiral symmetry characteristics.

Contribution

It introduces a relativistic Bogoliubov transformation framework for Majorana neutrinos, redefining charge conjugation and vacuum structure to better understand their properties.

Findings

Majorana neutrino can be viewed as a Bogoliubov quasiparticle.

Charge conjugation properties are modified via a Bogoliubov transformation.

Massless Majorana fermions exhibit chiral invariance.

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.