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My question concerns a comment made on this post:

Because one needs two Majorana modes $\gamma_1$ and $\gamma_2$ to each regular fermionic $c^\dagger c$ one, any two associated Majorana modes combine to create a regular fermion.

I understand the math behind this, but I would like a more physical understanding of why two Majorana zero modes make a fermion in a condensed matter system. Any additional reference that talks about these Majorana operators at the level of Fradkin's or Wen's book on field theory in condensed matter would be greatly appreciated.

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Joshuah Heath
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    It's just like the statement that one complex number contains the "information" of two real numbers. Complex is like regular fermion, real is like the Majorana fermion. It's the math but it's also the physics. It's not clear to me in what sense the physical explanation of this simple counting could be "completely different". At most, one may use different words for the same. – Luboš Motl Feb 21 '17 at 06:39
  • @LubošMotl Can we only "split" a Majorana fermion in the condensed matter sense? In both particle physics and condensed matter, a normal fermion is complex and a Majorana fermion is real. Does this mean we can similarly decompose a "real-world" fermion into its real, Majorana components? – Joshuah Heath Feb 21 '17 at 17:53
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    You probably meant splitting of a regular fermion, not a splitting of a Majorana one. But more generally, in condensed matter physics, there's no universal difference between elementary and composite particles so anything may be split when the environment is appropriately modified and basic conditions are obeyed. But you didn't obey the basic condition. In particular, the Grassmann parity is always preserved. You can't physically split 1 fermion into 2 fermions of any kind. A fermion times (=physical combination) a fermion is a boson. – Luboš Motl Feb 22 '17 at 05:19

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