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Coupling gauge theory to spinfoam 3d quantum gravity

  1. Jun 13, 2007 #1


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    Surely, I’m not the only one reading the links that you provide!
    Coupling gauge theory to spinfoam 3d quantum gravity
    Simone Speziale
    June 11, 2007
    Note: The Acknowledgments:
    The author is particularly grateful to Carlo Rovelli, Laurent Freidel, Hendryk Pfeiffer and John Barrett for many discussions and suggestions.
    Maybe, everyone only wants to read the simple presentations in my blog.
    Previous papers

    A semiclassical tetrahedron
    Carlo Rovelli and Simone Speziale_
    CPT†, CNRS Case 907, Universit´e de la M´editerran´ee, F-13288 Marseille
    Perimeter Institute, 31 Caroline St.N, Waterloo, ON-N2L-2Y5, Canada
    March 31, 2007

    Grasping rules and semiclassical limit of the geometry
    in the Ponzano–Regge model
    Jonathan Hackett and Simone Speziale
    17 Nov 2006
    Choosing the double tetra as a spinfoam 3d model is only the beginning of a long journey.
    Does anyone know if a baby elephant is born head first?

    QCD Phenomenology
    Lectures at the CERN–Dubna School, Pylos, August 2002
    Yu.L. Dok****zer
    The status of QCD phenomena and open problems are reviewed
    29 June 2003

    (Chiral Quark–Soliton Model (CQSM) )
    Nuclear matter in the chiral quark soliton model with vector mesons
    S.Nagai1, N.Sawado, and N.Shiiki1,
    (Dated: March 22, 2007)
    The idea of investigating dense nuclear matter in the topological soliton models has been developed over decades. It was first applied for the nuclear matter system with the skyrmion centered cubic (CC) crystal by Klebanov [1]. This configuration was studied further by W¨ust, Brown and Jackson to estimate the baryon density and discuss the phase transition between nuclear matter and quark matter [2]. Goldhabor and Manton found a new configuration, body-centered cubic (BCC) of half-skyrmions in a higher density regime [3]. The face centered cubic (FCC) and BCC lattice were studied by Castillejo et al. [4] and the phase transitions between those configurations were investigated by Kugler and Shtrikman [5]. Recently, the idea of using crystallized skyrmions to study nuclear matter was revived by Park, Min, Rho and Vento with the introduction of the Atiyah-Manton multi-soliton ansatz in a unit cell [6].

    The chiral quark soliton model (CQSM) can be interpreted as the soliton bag model including not only valence quarks but also the vacuum sea quark polarization effects explicitly [16, 17, 18, 19]. The model provides correct observables of a nucleon such as mass, electromagnetic value, spin carried by quarks, parton distributions and octet, decuplet SU(3) baryon spectra [20, 21].
    The following is a good explanations of the quark sea with the use of instantons
    06 may 2002
    Instanton fluctuations are characterized by their position in space-time zμ, the spatial size p and orientation in color space O, all in all by 12 collective coordinates.

    Note: It should be possible to link the double tetras to 12 instantons.
    ref. p.13 from http://arxiv.org/PS_cache/arxiv/pdf/0706/0706.1534v1.pdf

    The key diagram to evaluate is …. (see paper)
    This diagram has 4 x 36 = 144 contributions, coming from all the possible choices of graspings in a given point, times the four points. Each contribution can be evaluated using grasping rules and recoupling theory as in [8]. Because there are only double graspings entering this expression, the evaluation is rather simple and we do not report the details here, but only the asymptotics.
    Let us distinguish two types of terms, when the YM grasping is diagonal, namely s3 = t3, and when is not diagonal, namely s3 6= t3. Consider first the diagonal case. For fixed s3 = ij, there are 4 contributions from p = i, and four from p = j. To fix ideas, let us choose s3 = 12 ….

    The average size of instantons found in ref. 11 is ¯_ ≈ 0.36 fm and their average separation is ¯R = (N/V )−1 4 ≈ 0.89 fm. Similar results have been obtained by other lattice groups using various techniques. A decade earlier the basic characteristics of the instanton ensemble were obtained analytically from the Feynman variational principle 12,13 and expressed through the only dimensional parameter _ one has in QCD: ¯_ ≈ 0.48/_MS ≃ 0.35 fm, ¯R ≈ 1.35/_MS ≃ 0.95 fm, if one uses _MS = 280MeV as it follows from the DIS data.
    Summing up instanton-induced quark interactions in baryons leads to the Chiral Quark–Soliton Model where baryons appear to be bound states of constituent quarks pulled together by the chiral field. The model enables one to compute numerous parton distributions, as well as ‘static’ characteristics of baryons – with no fitting parameters.

    Numerous parton distributions have been computed in the CQSM, mainly by the Bochum group. 27,28,29 There have been a number of mysteries from naive quark models’ point of view: the large number of antiquarks already at a low virtuality, the ‘spin crisis’, the large flavor asymmetry of antiquarks, etc.
    The CQSM explains all those ‘mysteries’ in a natural way as it incorporates, together with valence quarks bound by the isospin-1 pion field, the negative energy Dirac sea. Furthermore, the CQSM predicts nontrivial phenomena that have not been observed so far: large flavor asymmetry of the polarized antiquarks 29, transversity distributions 30, peculiar shapes of the so-called skewed parton distributions 31 and other phenomena in hard exclusive reactions. 32
    Baryon dynamics is rich and far from naive “three quarks” expectations.
    What is the popularity of the Chiral Quark–Soliton Model (CQSM)?
    Has the addition of the INSTANTONS to explain the “quark sea” been received as a positive step?
    Has anyone been able to make the connection with the Chiral Quark–Soliton Model (CQSM) and spinfoam or 12 INSTANTON TO THE DOUBLE TETRAS?

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  3. Jun 13, 2007 #2


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    Jal, you flagged another good one. Speziale is one of the principle researchers working in spinfoam.

    He is wrapping QG and Yang-Mills into one spinfoam package, and getting it to work in a simplified case. It is quite remarkable that he could do this. The paper initiates a kind of thrust into new territory and we have to watch to see how things progress along the way it defines.

    He gives some preview of future work in the conclusions:

    "...Another important question for future work is how to restore the full diffeomorphism invariance of the continuum theory, here broken by the choice of a fixed triangulation. The model being non-topological, the symmetry should be restored by including a sum over the triangulations, for instance along the lines of the group field theory approach [23]..."

    He also cites a paper by Etera Livine, Dan Oriti and others that is "to appear".

    "...M. Karadi, E. R. Livine, D. Oriti and J. Ryan, “Effective non-commutative field theory for spinning particles coupled to 3d quantum gravity,” to appear."

    this paper deals with the riemannian case in 3D, which means trying to extend the results to the lorentzian case, and if possible to 4D.
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