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I'm trying to understand the basics of anyons physics. I understand there is neither a Fock space they live in (because Fock is just the space of (anti-)symmetrized tensor product state, see e.g. Wikipedia), nor a (pseudo / fictitious) commutation relation for them, as discussed at this Phys.SE post. But still I've a few questions regarding their statistics:

  • Can we associate a creation / destruction operator to an anyon mode ? Does it make sense to talk about mode of anyons?

  • Is there a general occupation function like Fermi-Dirac or Bose-Einstein for fermions or bosons ? Is it model dependent, i.e. does it depend on the type of anyon ? Does it make sense to discuss number of anyons?

  • What is the ground state of anyons, like a Fermi sea or a Bose-Einstein condensate for fermions or bosons ? Does it make sense to talk about a ground state of a gas of anyons?

I believe this bunch of questions can all be contracted to

  • Does it make sense to talk of the anyons as particles ?

Because in principle a particle exists independently of the Fock space construction, isn't it ? We could still construct a space of the tensor product of non (anti-)symmetrised states.

I realised that a perhaps better approach on the question would be:

  • To which extend is the anyon statistic a (quantum) statistic ?

provided the two other quantum statistics I know (Bose and Fermi) provide a ground state, an occupation number, and some second-quantised version of operators.

Post-scriptum : This Phys.SE question is partially related to mine.

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@Qmechanic Thanks for the corrections, it's really easier to read now :-) – FraSchelle May 23 '13 at 22:11
Have you found yourself the answer? This question is really old, and I'm curious myself; if you've found the answer already, please write it, because I really want to know more about this topic. – Vendetta Oct 30 '15 at 18:35
@Vendetta Unfortunately not, otherwise I would have written the answer. Thanks for your interest in this question. I've tried to add an other tag, to see if more people will see it :-) – FraSchelle Oct 31 '15 at 11:35

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