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Topological order - string-net condensation + loop quantum gravity

  1. Sep 16, 2007 #1


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    I've just read
    Quantum field theory of many-body systems
    Xiao-Gang Wen
    His web page
    I thought that his book might be easier than his papers. hehehe It's a text book.
    I did get to learn a few things.

    Here is what wiki says about the subject.

    In physics, topological order is a new kind of order (a new kind of organization of particles) in a quantum state that is beyond the Landau symmetry-breaking description.
    Why is topological order important? Landau symmetry-breaking theory is a cornerstone of condensed matter physics. It is used to define the territory of condensed matter research. The existence of topological order appears to indicate that nature is much richer than Landau symmetry-breaking theory has so far indicated. The exciting time of condensed matter physics is still ahead of us. Some suggest that topological order (or more precisely, string-net condensation) has a potential to provide a unified origin for photons, electrons and other elementary particles in our universe.
    For strings labeled by the positive integers, string-nets are the spin networks studied in loop quantum gravity. This has led to the proposal by Wen and Levin, [1] , and Smolin, Markopolou and Tomasz, [2] that loop quantum gravity's spin networks can give rise to the standard model of particle physics through this mechanism, along with fermi statistics and gauge interactions. To date, a rigorous derivation from LQG's spin networks to Wen's spin lattice has yet to be done.

    I found the following trying to make the relationship with LQG
    Quantum Graphity
    Tomasz Konopka, Fotini Markopoulou, Lee Smolin
    (Submitted on 17 Nov 2006) )
    “We argue (but do not prove) that under certain conditions the spins in the system can arrange themselves in regular, lattice-like patterns at low temperatures. When the graph is frozen, the model is closely related to a model of Levin and Wen [4, 5, 6] which has emergent gauge degrees of freedom.”
    “…it is helpful to first consider the graph of “on” links to be frozen in a particular configuration, say a regular cubic lattice where the minimal loops in the graph are plaquettes. In this case, these terms reduce to the rotor model of Levin and Wen [6]”
    Xiao-Gang Wen ends his book with the following:
    “What is the origin of gauge field – geometrical or dynamical?
    What is the origin of Fermi statistics – given or emergent?
    In this book, we favor the dynamical and emergent origin of gauge bosons and fermions. The gauge bosons and the Fermi statistics may just be collective phenomena of quantum many-boson systems, and nothing more.”
    Has anyone got any other link that try to make the relationship with LQG?
  2. jcsd
  3. Sep 18, 2007 #2


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    From reading some of Lee Smolin's latest papers, and his students, I get the impression that he is aware of Xiao-Gang Wen's work and that he is trying to combine LQG with QCD.
    See his presentation at Loop 07
    Has he identified any problem that might be insurmountable?
  4. Sep 18, 2007 #3


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    We did a discussion at https://www.physicsforums.com/showthread.php?t=161868
    The universe as a "string-net liquid"
    p. 472
    Xiao-Gang Wen uses 2 cubes with position #1 plaquete is shared by both cube OR is there two plaquete in the same position. Therefore, he has 11 positions for the fermions.
    If he was to expand to more than two cubes then all the plaquete positions would be shared/doubled. There would never be a certainty of minimum distance between the plaquetes or a certainty on the number of plaquetes.
    Cubic packing does not preserve the identity of each plaquete.
    Cubic packing does not preserve minimum length.
    His math might works (I’ll let others decide) but his picture of having cubes (a cubic lattice) will not work but it is close to being right. (after all, cubic packing and hex. packing preserve the volume.)
    However, by using hex. packing in 3d packing you get the 12 plaquete positions and they would not be shared and you would be able to keep minimum distances and the math should work with that picture.
    As a result, you can use the double tetra, (LQG, spin nets) because in the center of the spinning plaquetes is the double tetra.

    New directions
    in Background Independent
    Quantum Gravity
    Fotini Markopoulou
    20 March 2007
    1) Is spacetime geometry and general relativity fundamental or emergent?
    2) Is spacetime geometry, if present, dynamical or fixed?

    Our main focus in this chapter is a new, fourth, category that is currently under development and constitutes a promising and previously unexplored direction in background independent quantum gravity. This is pre-geometric background independent approaches to quantum gravity. These start with an underlying microscopic theory of quantum systems in which no reference to a spatiotemporal geometry is to be found. Both geometry and hence gravity are emergent.
    Note: Minimum length scale imposes a geometry.
    Xiao-Gang Wen said in his book that his model could be applied to QCD but he did not develop it.
    Is Lee Smolin trying to make the link of LQG and QCD?

  5. Sep 18, 2007 #4

    Is Lee Smolin trying to make the link of LQG and QCD?

    Where is Smolin expressly trying to do this?

    I wonder which research direction is most promising for combining LQG + SM = TOE

    preon braiding, (i.e Sundance)
    condense matter (i.e Wen)
    noncommuative geometry (i.e Connes)
    4D "string" (i.e Baez)
  6. Sep 18, 2007 #5


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    I like your short-list of research directions. All could succeed, and turn out to be equivalent versions so I will not try to pick the best (likewise all could fail but I see no clear loser either---they are all worth exploring.)

    Just to keep track of progress---there is some news or rumor about putting LQG together with Connes NCG. You can see what the program is in Grimstrup's latested paper but this is already a year old. I think some important progress has been made on that program which hasn't gotten put on arxiv yet. So I will just recall last year's paper to give an idea of the program:
    Intersecting Connes Noncommutative Geometry with Quantum Gravity
    Johannes Aastrup, Jesper M. Grimstrup
    19 pages, 4 figures
    (Submitted on 18 Jan 2006)

    "An intersection of Noncommutative Geometry and Loop Quantum Gravity is proposed. Alain Connes' Noncommutative Geometry provides a framework in which the Standard Model of particle physics coupled to general relativity is formulated as a unified, gravitational theory. However, to this day no quantization procedure compatible with this framework is known. In this paper we consider the noncommutative algebra of holonomy loops on a functional space of certain spin-connections. The construction of a spectral triple is outlined and ideas on interpretation and classical limit are presented."


    the goal is to build a spectral triple on the space of connections (realized as a limit of productgroups Gn)

    to understand Grimstrup and Aastrup's work one must know what a spectral triple is---it is the basic object in Connes NCG where he derives the Standard Model from a certain spectral triple.

    If Grimstrup et al can make a spectral triple that meets Connes specifications and which is based on a space of spacetime geometries (i.e. on a space of connections) then it can include both a version of LQG and also the essentials of Particle Physics.

    this is why I think it would be good to glance at the above paper, even though it is a year old and only describes work-in-progress

    thanks to both of you for keeping an alert watch. Ensabah's list is a good one I think. EACH approach to the goal should be watched IMO.
  7. Sep 18, 2007 #6


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    Hi ensabah6
    Is Lee Smolin trying to make the link of LQG and QCD?

    Where is Smolin expressly trying to do this?

    Look at his Physics talks and you tell me.
    • Particle physics from quantum gravity (Spring 2006)
    • Emergence of chiral matter from quantum gravity ('t Hooft conference, summer 2006
    Hi Marcus

    At the end of the day there has to be a dynamic structure.
  8. Sep 18, 2007 #7
    Well thanks Marcus.

    Considering that Alaine Connes is the founder of NCG, and Carlo Rovelli is a major LQG researcher, authoring a textbook in the subject, and Rovelli and Connes are friends and correspondants, has Alaine Connes weighed in some sort of QG for NCG -- for example a LQG+NCG?

    For example, would a QG of NCG change his prediction for the higgs boson mass of 170 GEV? Would a NCG of LQG help identify its SC limit? For that matter have other LQG-NCG researchers weighed in on Grimstrup and Aastrup work?
    Last edited: Sep 18, 2007
  9. Sep 20, 2007 #8
    I forget to mention
    Stephen Alexander's paper "lqg and electroweak unification"
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