In 1937, italian physicist Ettore Marojana modified the Dirac equation so that it would admit only real solutions (as opposed to complex-valued solutions). Such solutions are known as Majorana fermions, a class of particles that are interestingly their own anti-particles. Recently, Majorana fermions have migrated into condensed matter physics, as they have been predicted to occur as elementary excitations of systems containing many interacting fermions. In particular, they are predicted to exist in chiral p-wave superconductors, in superfluid 3He, and for the so-called Moore-Read Pfaffian state thought to be realized for some fractional quantum Hall states. The interest for the Majorana
fermions is largely driven by that they obey to non-abelian braiding quantum statistics, a necessary property for the construction of a topological quantum computer that would, in principle, be immune to local perturbations.
In this talk, I will briefly review the recent progress in the field of non-abelian quantum statistics with a strong emphasis on the physics of the "5/2" fractional quantum Hall state where such statistics are thought to occur. In particular, I will discuss the conundrum of the spin polarization for that state, as well as discussing the hypothetical adiabatic cooling of non-abelian states which could be used as an experimental proof of "non-abelianness".