On the Geometric Phase and Majorana Neutrinos

We analyze the geometric phase for neutrinos and we demonstrate that the geometric invariants associated to transitions between different neutrino flavors, for Majorana neutrinos, can depend on the representation of the mixing matrix and then 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 in principle be used as tools to distinguish between Dirac and Majorana neutrinos.