When a topological order is realized in a certain class of superconductors, it supports Majorana fermions on the edge or in the vortex core. Vortices with Majorana fermion modes are neither fermions nor bosons but non-Abelian anyons, obeying the non-Abelian statistics for which the exchange operations of particles are not commutative. Because of this remarkable feature, Majorana fermions plays ...

In many mathematical and physical contexts spinors are treated as Grassmann odd valued fields. We show that it is possible to extend the classification of reality conditions on such spinors by a new type of Majorana condition. In order to define this graded Majorana condition we make use of pseudo-conjugation, a rather unfamiliar extension of complex conjugation to supernumbers. Like the symple...

There are physical Majorana phases in the lepton flavor mixing matrix when neutrinos are Majorana fermions. In the case of two degenerate neutrinos, the physical Majorana phase plays the crucial role for the stability of the maximal flavor mixing between the second and the third generations against quantum corrections. The physical Majorana phase of π guarantees the maximal mixing to be stable ...

In 1937 the Italian physicist Ettore Majorana proposed the existence of a massless, chargeless, spinless particle that is its own antiparticle. Such a Majorana fermion would have an extraordinarily large phase coherence time, making it an ideal building block for a quantum computer. However, no Majorana fermions are known to exist asfundamental particles. The recent discovery of topological sta...

Luteinizing hormone-releasing hormone (LHRH) neurons and fibers are located in the anteroventral hypothalamus, specifically in the preoptic medial area and the organum vasculosum of the lamina terminalis. Most luteinizing hormone-releasing hormone neurons project to the median eminence where they are secreted in the pituitary portal system in order to control the release of gonadotropin. The ai...

We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in the proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relati...

There are Poincare group representations on complex Hilbert spaces, like the Dirac spinor field, or real Hilbert spaces, like the electromagnetic field tensor. The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana spinor field is a space-time dependent Majorana spinor, solution of the free Dirac equation. The Majorana-Fourier and Majorana-Hankel transforms of Majo...

A demonstration that the observed neutrinos are not Majorana particles Abstract It is shown that Majorana neutrinos cannot couple vectorially to the neutral-current SU(2) L x U(1) gauge field of the standard model. Since strong evidence for the existence of such a vector coupling in neutral current reactions has recently been presented by the Charm II collaboration, it is unlikely that the obse...

In this paper we study unitary braid group representations associated with Majorana Fermions. Majorana Fermions are represented by Majorana operators, elements of a Clifford algebra. The paper recalls and proves a general result about braid group representations associated with Clifford algebras, and compares this result with the Ivanov braiding associated with Majorana operators. The paper gen...