Ok my understanding of the Fermion, Boson difference is this:(adsbygoogle = window.adsbygoogle || []).push({});

Identical Particles carry a representation of the permutation group. Since we have not found any para statistics, this representation must be one dimensional. And there are only two one dimensional irreducible representations of the permutation group: the identity and sign(P). Depending on the representation we are dealing with Bosons or Fermions.

In 3d we can permute particles by moving them in space, and if the space is simply connected there can be no "orientation" in these swaps.

In 2d this is different. And now I don't really know how to make the connection. There is the claim, that one has to replace the permutation group with its simply connected extension aka Atkin's braid group, allowing for more statistics and there is the claim that this helps in understanding the fractional quantum Hall effect.

But I don't understand how confining an electron is supposed to allow it to change its statistics. The world is still three dimensional. Confinement cannot change this.

- So what are we talking about here? Electron excitations?

- Can the braid group statistics even be constructed from particles that don't adhere to them individually?

- And if it can what makes people think that the solid state environment will jump through what looks like very elaborate hoops to make anyon statistics work?

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# Understanding of the Fermion, Boson difference

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