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My knowledge of quantum mechanics is rather limited, but what I always understood was that Bosons have integer spins and Fermions have half-integer spins.

My question is very simple: the Majorana particle has no spin according to this paper and this Physics Today article which (without wanting to go into a philosophical mathematical discussion) I would call integer spin. That would make the particle a Boson. So what is the reason that the particle is classified as a Fermion?

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Do you have a source for the statement that Majorana particles have no spin? –  Chris White Feb 19 '13 at 6:35
Here: arxiv.org/abs/1209.5115 or here: physicstoday.org/resource/1/phtoad/v65/i6/p14_s1 In particular, the last post has a sentence saying: "As quasiparticles go, the Majorana is incredibly featureless: It’s chargeless, spinless, massless, and without energy" –  Michiel Feb 19 '13 at 6:51
Michael, you're actually wrong. Majorana fermions are defined as fermions that are complex conjugate to themselves, but they don't have to be created by spinor fields. In fact, the arxiv.org/abs/1209.5115 case has spinless Majorana fermions, indeed. This would contradict the spin-statistics theorem in a Lorentz-invariant theory but this condensed-matter application isn't Lorentz-invariant, so one may encounter spinless fermions. –  Luboš Motl Feb 19 '13 at 7:47
Dear Lubos, could you elaborate your comment a bit (perhaps in a full-blown answer) because I am not sure whether I completely understand your comment. You say they are spinless, because they can be complex conjugates without creation by spinor fields. Then what is it that causes them to be complex conjugates? –  Michiel Feb 19 '13 at 8:02
@LubošMotl I stand corrected. I was coming from a particle physics perspective, unfamiliar with the conventions in condensed matter. I deleted my old comment to avoid future confusion. –  Michael Brown Feb 19 '13 at 10:58

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up vote 8 down vote accepted

Majorana fermions are by definition fermions which are their own antiparticles, i.e. the do have spin and it's 1/2. An introduction to these fermions can be for example found here: http://arxiv.org/abs/0806.1690. In contrast bosons are their own antiparticles, e.g. photons, i.e. one does not need a "Majorana-boson" definition.

Now, one has to say that these Majorana fermions have not been observed in nature except as quasiparticle excitations in seminconductors.

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"one has to say that these Majorana fermions have not been observed in nature except [...]" Well, we've observed neutrinos and don't yet know if they are Dirac or Majorana, so let's say "have not been demonstrably observed" or some such weasel word. –  dmckee Feb 19 '13 at 7:10
For completeness: Majorana fermions where recently observed (though indirectly) by the group of Leo Kouwenhoven in Delft –  Michiel Jun 26 at 19:56
Bosons are not in general their own antiparticles -- e.g. the W+ boson has a distinct W- boson as its antiparticle. Nevertheless, a Majorana particle always seems to refer to a fermion. –  mortenpi Oct 3 at 17:52

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