We study the implications of neutrino oscillations with maximal mixing for the neutrino Dirac and Majorana matrices in the see-saw mechanism for three non degenerate neutrino masses. We find the form of the Dirac matrix for a structure-less Majorana matrix and, conversely, the structure of the Majorana matrix if the Dirac matrix is according to our naive intuition. We give some examples of Majo...

DRAFT VERSION The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor representations of the Rotation and Lorentz groups are irreducible. The spinor fields are space-time dependent spinors, solutions of the free Dirac equation. We define the Majorana-Fourier transform and relate it to the linear momentum of a spin one-half Poincare group representation. We sh...

We report on theoretical courses by Fermi and Majorana, giving evidence of the first appearance and further development of Quantum Mechanics teaching in Italy. On the basis of original documents, we make a comparison between Fermi’s and Majorana’s approaches. A detailed analysis is carried out of Fermi’s course on Theoretical Physics attended by Majorana in 1927-28. Three (previously unknown) p...

Majorana fermions are zero-energy quasiparticles that may exist in superconducting vortices and interfaces, but their detection is problematic since they have no charge. This is an obstacle to the realization of topological quantum computation, which relies on Majorana fermions to store qubits in a way which is insensitive to decoherence. We show how a pair of neutral Majorana fermions can be c...

We show that Majorana particles belong to the Wigner class of fermions in which the charge conjugation and the parity operators commute, rather than anticommute. Rigorously speaking, Majorana spinors do not satisfy the Dirac equation [a result originally due to M. Kirchbach, which we re-render here]. Instead, they satisfy a different wave equation, which we derive. This allows us to reconcile S...

Majorana fermion is a hypothetical particle that is its own antiparticle. We report transport measurements that suggest the existence of one-dimensional chiral Majorana fermion modes in the hybrid system of a quantum anomalous Hall insulator thin film coupled with a superconductor. As the external magnetic field is swept, half-integer quantized conductance plateaus are observed at the locations...

In this paper, we suggest an alternative strategy to derive the complex two-component Majorana equation with a mass term and elucidate the related Lorentz transformation. The Majorana equation is established completely on its own, rather than derived from the chiral Dirac equation. Thereby, use is made of the complex conjugation operator and Pauli spin matrices only. The eigenfunctions of the t...

As an attempt to understand and search for the existence of Majorana zero mode, we study the topological quantum phase transition and also the nature of this transition in helical liquid system, which appears in different physical systems. We present Majorana-Ising transition along with the phase boundary in the presence of interaction. We show the appearance of Majorana mode under the renormal...

The most plausible see-saw explanation of the smallness of the neutrino masses is based on the assumption that total lepton number is violated at a large scale and neutrinos with definite masses are Majorana particles. In this review we consider in details difference between Dirac and Majorana neutrino mixing and possibilities to reveal Majorana nature of neutrinos with definite masses.