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Fractional quantum Hall effect, Anyon, Sundance Bilson-Thoompson

  1. Sep 10, 2009 #1
    Could Anyons and Fractional quantum Hall effect create 2-D ribbons w/fractional electric charge (e/3) that combine to form fermions or bosons?

    Sundance Bilson-Thompson proposed a braiding model of 3's which could account for some particles of the standard model (i.e first generation fermions and bosons)
  2. jcsd
  3. Sep 11, 2009 #2
    -What do you mean by "A braiding model of 3's" ?

    Anyons arise in the Fractional Quantum Hall Effect, yes. But they arise as point particles - not as ribbons. Unless you view them in the complete (2+1)-dimensional space ofcourse. In that case a point particle traces out a world-line, and due to regularization this lineis viewed as a ribbon. Is that what you mean?

    So, please, be a bit more specific in your question.
  4. Sep 11, 2009 #3
    Could they combine to form fermions or bosons?
  5. Sep 11, 2009 #4
    Yes they can. When the anyons are brought together they combine through a process what is called fusion. The mathematical structure underlying this process is called a fusion algebra (related to quantum groups and topological field theories). They fusion algebra is somtehing like a group, in that it closes on itself. It's also finite (i.e. contains a finite number of anyons), and in the FQHE it includes also bosons and fermions. Fusing two anyons gives another anyon. So yea, you it is very well possible that you end up with the boson or fermion upon fusing.

    From a more physical persepective this is also quite natural. The anyons arise as collective excitations out of the electrons. So when you mix these excitations together, it should not be too suprising you can construct an electron out of it - it is after all these particles which are the constituents in the first place.
  6. Sep 11, 2009 #5
    Is it possible to create an analog system where either space itself or a condensate fluid like field permeating space could create these anyons which can combine to form the SM particles?
  7. Sep 12, 2009 #6
    That probably generates more problems than it would solve. You would need the emergence of gauge fields and gauge potentials, different flavor symmetries, and a mechanism that get rids of the anyons as allowed particles.

    Let alone the fact that we are talking about a strict 2+1 dimensional system. Anyons are point particles, and the only reason they can exist in the first place is because of this specific dimension. The extension of these condensates to 3+1 dimensions is not a trivial matter (although certain classes exist, that fall under the name of topological insulators).

    But the anyons are just a by-product of these types of phases (topological phases). You shouldnt be focussing on the anyons to fix the problems, but rather on the underlying symmetry structures. For instance, maybe try to generalize the notion of quantum groups to higher dimensions. There are models which have been put forth that deal with this type of emergence - models which exhibit topological behavior and in which gauge fields and fermions emerge, rather than being fundamental. Try looking up the Levin and Wen models.
  8. Sep 12, 2009 #7
    I'm glad you mention Levin and Wen models, I know he attempts to ground some aspects of the SM in emergence, what do you think of his attempt? Can his attempt explain some of the unknown 18 parameters of the SM, including masses, 3 generations, Weinberg mixing angles? What is it about his emergence models that prevents chiral neutrinos and chiral coupling to W and Z gauge bosons?
  9. Sep 13, 2009 #8
    It's nowhere near, but it's not intended to be. The work is really more a philosophical statement rather than an attempt to re-create the SM. It's saying that there's nothing fundamental about fermions and gauge bosons, and that these can emerge as the low energy excitations of some other _unspecified_ problem. It's showing that universality can extend to these systems, which at one time or another had been felt to be so constrained by their respective symmetries that any underlying microscopic theory had to respect those symmetries also.

    In Wen's book, he paints, I think, a rather optimistic view point of how far this can be extended. He identifies a few remaining puzzles, chiefly amongst them the issue of how to get chiral fermions and gravity. But it's important to realise that even if it turns out to be possible to have these emerge (and I do think it's likely --- gravity + bosonic field has been done, not sure about fermions), it only makes constraining the microscopic theory behind SM _harder_, not easier.

    Incidentally, the view of gauge theories as lines connecting two fermions has been around for about four or five decades. After all, it's clear that whilst the connection, as a classical variable, is not gauge invariant, various quantities like Wilson loops (and its extension to the non-Abelian case, or open strings terminated by fermions) were realised very early on to be gauge invariant. Further work, mostly using QED (which is unfortunately much simplified from the full case) has shown that it's possible to entirely base the theory on these loop variables --- up to certain mathematical complications due to the need to smear the loops slightly. In fact, this line of attack is what eventually gave string theory (though it can be argued that string theory deviated a little from the spirit of things). Similarly in loop quantum gravity, the idea to to rephrase GR in terms of loop/gauge invariant variables. However, these are all classical variables, and thus suffer from all sorts of rather nasty singular behaviour even when the quantum theory is well-defined.
  10. Sep 13, 2009 #9


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    Probably off on a tangent, but I've wondered if the Nielsen-Ninomiya theorem and the Ginsparg-Wilson relation have anything to do with it.
  11. Sep 13, 2009 #10
    interesting. Even string theory suffers from singular behavior? I've not heard this before.
  12. Sep 14, 2009 #11
    No; I mean that attempts to use loop variables for a classical theory leads to singularities. The quantum theories naturally "smear" things enough for a separable Hilbert space to be constructed.
  13. Sep 14, 2009 #12
    One criticism I've heard of LQG is that the Hilbert space is non-separable.

    How do you feel about Volvovik's proposal and how does it relate to what Wen is doing?
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