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.