On the geometric phase for Majorana and Dirac neutrinos

Abstract

Abstract We analyze the geometric phase for neutrinos and we demonstrate that the geometric invariants associated with transitions between different neutrino flavors, for Majorana neutrinos, are not left unchanged by rephasing transformations and are sensitive to the nature of neutrinos. The dependence of geometric invariants on the Majorana phase cannot be eliminated by a charged lepton rephasing transformation. By considering kinematic and geometric approach we also demonstrate that the Majorana phase is relevant in the projective Hilbert space. Geometric invariants can therefore be used as tools to distinguish between Dirac and Majorana neutrinos.