Would a successful merger of LQG + NCG SM be considered a TOE?

  1. LQG is an attempt to quantize geometry

    Noncommutative geometry is an attempt to express the SM geometrically, and is able to derive the SM Lagrangian and prediction of Higgs mass.

    LQG is not a TOE since it does not include SM, only quantize gravity, and NCG is not a TOE since it does not include a quantum theory of gravity.

    There have been a variety of papers by Aastrup, Marcolli, etc., to merge NCG with LQG, to peserve the NCG spectral triples and hence SM lagrangians and quantized geometry.

    LQG and NCG are both "geometrical", neither is a TOE.
    Would the merger of LQG with NCG be considered a TOE, and if so, how does it contrast/compare with string theory and GUT's as TOE?

    Perhaps Loop Quantum Gravity + Noncommutative geometry should be called Loop Quantum GEOMETRY or Noncommutative Loop Geometry.

    I'm surprised that thus far this project has very limited traction.

    references:

    http://arxiv.org/pdf/1005.1057

    http://arxiv.org/abs/1005.1057
    Spin Foams and Noncommutative Geometry
    Domenic Denicola (Caltech), Matilde Marcolli (Caltech), Ahmad Zainy al-Yasry (ICTP)
    48 pages, 30 figures
    (Submitted on 6 May 2010)
    "We extend the formalism of embedded spin networks and spin foams to include topological data that encode the underlying three-manifold or four-manifold as a branched cover. These data are expressed as monodromies, in a way similar to the encoding of the gravitational field via holonomies. We then describe convolution algebras of spin networks and spin foams, based on the different ways in which the same topology can be realized as a branched covering via covering moves, and on possible composition operations on spin foams. We illustrate the case of the groupoid algebra of the equivalence relation determined by covering moves and a 2-semigroupoid algebra arising from a 2-category of spin foams with composition operations corresponding to a fibered product of the branched coverings and the gluing of cobordisms. The spin foam amplitudes then give rise to dynamical flows on these algebras, and the existence of low temperature equilibrium states of Gibbs form is related to questions on the existence of topological invariants of embedded graphs and embedded two-complexes with given properties. We end by sketching a possible approach to combining the spin network and spin foam formalism with matter within the framework of spectral triples in noncommutative geometry."

    http://arxiv.org/abs/0907.5510

    On Semi-Classical States of Quantum Gravity and Noncommutative Geometry
    Authors: Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke, Ryszard Nest
    (Submitted on 31 Jul 2009)

    Abstract: We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian in 3+1 dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our analysis shows that the model might contain fermionic matter degrees of freedom.
    The semi-classical analysis presented in this paper does away with most of the ambiguities found in the initial semi-finite spectral triple construction. The cubic lattices play the role of a coordinate system and a divergent sequence of free parameters found in the Dirac type operator is identified as a certain inverse infinitesimal volume element.


    Intersecting Connes Noncommutative Geometry with Quantum Gravity
    Authors: Johannes Aastrup, Jesper M. Grimstrup
    (Submitted on 18 Jan 2006)

    Abstract: 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.
     
  2. jcsd
  3. Well... first of all, LQG needs still needs to be convincingly shown that it leads to 4d gravity in flat space in the first place. Second the NC approach of Connes et al represents a parametrization of the SM, not a derivation. It does not explain why the standard model comes out and no other gauge theory. This is the vacuum selection problem in disgiuse. Its prediciton of the Higgs mass is moot, this just refers to some well known renormalization properties of the SM. Moreover its quantum mechanical consistency, when coupled to gravity, is unclear.

    Thus, there are good reasons why by far the majority of professional particle physicists do not follow this route, but rather something that the armchair scientists over here don't like.
     
  4. According to the paper cited below, though, combining LQG + NCG changes the properties, for example, the non-separable Hilbertspace in LQG is separable in his LQG+NCG construction

    Since in order for LQG to be a serious candidate of physics, it needs to incorporate SM-QFT matter. The papers are to this effect, are there any reasons why this approach is not sound?


    http://arxiv.org/abs/0907.5510

    On Semi-Classical States of Quantum Gravity and Noncommutative Geometry
    Authors: Johannes Aastrup, Jesper M. Grimstrup, Mario Paschke, Ryszard Nest
    (Submitted on 31 Jul 2009)

    Abstract: We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian in 3+1 dimensions. Also, time-independent lapse and shift fields emerge from the semi-classical states. Our analysis shows that the model might contain fermionic matter degrees of freedom.


    http://arxiv.org/abs/hep-th/0601127
    Intersecting Connes Noncommutative Geometry with Quantum Gravity
    Authors: Johannes Aastrup, Jesper M. Grimstrup
    (Submitted on 18 Jan 2006)

    Abstract: 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 semi-classical analysis presented in this paper does away with most of the ambiguities found in the initial semi-finite spectral triple construction. The cubic lattices play the role of a coordinate system and a divergent sequence of free parameters found in the Dirac type operator is identified as a certain inverse infinitesimal volume element.
     
  5. tom.stoer

    tom.stoer 5,489
    Science Advisor

    I think this has been shown for the Graviton propagator by Rovelli et al.

    Afaik NGC is a special choice for a nc structure; but I was thinking that Connes found some reasons why this special structure should be preferred. Are there some new results on these topics?

    I thought this was one of the strengths of his approach ...
     
  6. Connes has been very clear about what he puts in and what he gets out. It is quite unfair to read that his prediction is "moot" while most mainstream approach did not care/dare to come up with specific numbers.

    The fair statement is that the majority of physicists do not follow Connes route because they do not understand it, and the main contribution of suprised is to illustrate this fact.
     
  7. tom.stoer

    tom.stoer 5,489
    Science Advisor

    I saw many post of humanino; none of them was ridiculous. The only ridiculous and arrogant post in this thread is yours.
     
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