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How similar is Wen's spin lattice model to LQG's 4D spin foam theories?

  1. Apr 17, 2007 #1
    Is there a way to get a local bosonic theory out of spin foam formalism?

    Xiao-Gang Wen's suggestion, first published 6 Jul 2004
    http://arxiv.org/abs/cond-mat/0407140v2 Page 8
    "Remarkably, it appears that the theory of loop
    quantum gravity can be reformulated in terms of a
    particular kind of string net [condensation]...in
    addition to gauge interactions and Fermi statistics,
    string net condensation can give rise to gravity"

    Is there a way to get a local bosonic theory out of spin foam formalism?

    If you can connect spin foam formalism with Wen's
    string-net derivation, you can get gravity and the
    standard model.

    http://dao.mit.edu/~wen/NSart-wen.html

    "So in their theory elementary particles are not the
    fundamental building blocks of matter. Instead, they
    emerge as defects or "whirlpools" in the deeper
    organized structure of space-time."

    "Now this problem is solved. If the spins that form
    our space organize into a string-net liquid, then the
    collective motions of strings give rise to light waves
    and the ends of strings give rise to electrons. The
    next challenge is to find an organization of spins
    that can give rise to gravitational wave."


    How hard would it be to get from 4D spin foams to
    Wen's string-nets "lattice spin models"
    http://dao.mit.edu/~wen/pub/qorder.html?

    http://dao.mit.edu/~wen/pub/cosmos.html

    An artistic summary of the result:
    The following picture
    has mountain, lake, trees, snow,... ..., and light.

    If we look closer, we see atoms, electrons, protons, and photons.

    If we look even closer (I mean really really close), we see ...
    boring spins on a lattice.

    How can a simple boring spin system produce such a nice scenery?
    The answer is "more is different". When many quantum spins interact with each other, the spins can get organized (or entangled). The pattern of organization is called quantum order. It is this pattern (ie the quantum order) of spins that makes wonders. The twists and defects in the pattern correspond to "elementary" particles. In this way, quantum order produces electrons, photons, atoms, ... ..., and the beautiful scenery.
    (4/2002)


    He's recently published how to get gravitons from a "spin" model.
    arXiv:gr-qc/0606100 [ps, pdf, other] :
    Title: A lattice bosonic model as a quantum theory of gravity
    Authors: Zheng-Cheng Gu, Xiao-Gang Wen
    Comments: 4 pages. RevTeX4. Homepage this http URL

    Could spin foam theorists make use of his results directly into their own models?

    Both make use of wilson lines, wilson loops, simon-cherns theories, etc.

    http://arxiv.org/abs/cond-mat/0407140v2

    Recent advances in condensed matter theory have revealed that new and exotic phases of matter can exist in spin models (or more precisely, local bosonic models) via a simple physical mechanism, known as "string-net condensation." These new phases of matter have the unusual property that their collective excitations are gauge bosons and fermions. In some cases, the collective excitations can behave just like the photons, electrons, gluons, and quarks in our vacuum. This suggests that photons, electrons, and other elementary particles may have a unified origin -- string-net condensation in our vacuum. In addition, the string-net picture indicates how to make artificial photons, artificial electrons, and artificial quarks and gluons in condensed matter systems.
     
    Last edited: Apr 17, 2007
  2. jcsd
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