I am trying to understand the first 5 pages of Introduction to topological superconductivity and Majorana fermions http://arxiv.org/abs/1206.1736
I read it 2-3 times and thought about it but a few things still confuse me about the Kitaev chain.
1) We want Majorana-Fermions (MF) from this model. Fermions are 3D particles, but MF is a Non-Abelian Anyonen which is a 2D only particle. This already seems to make no sense. We construct with the Kitaev Chain a 1D system (a chain) and want to find there a 2D only particle? Technically, I guess it should even be 0D since the MF only shows up at the end of the chain. How is this supposed to make sense?
2) We rewrite the chain from the c fermion (electrons?) into a chain of MF and than again in form of another type of fermion $\tilde c$. How does this change the physical stuff the chain is made of? How do we translate this math-trick into a physical thing?
3) It is stated that a MF can be thought of as a electron and a hole. It is also stated that two MF can make any fermion. So an electron can be thought of as two MF which in turn can be thought of as an electron + hole. So one electron is two electrons and two holes?