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What is group field theory? Introduction please?

  1. Jul 14, 2010 #1
    wikipedia says



    Group field theory is a theory of quantum gravity. It is closely related to background independent quantum gravity approaches such as loop quantum gravity and spin foam and causal dynamic triangulation.

    It makes use of spin networks as simplex and uses quantum field theory to create a feynman graph over Simplicial manifold

    Is this correct?

    What is group field theory? What is its relation to LQG, SF, CDT, string theory? What does it try to do and why has it not received much press? What is the goal of group field theory? How does it intend to make contact with physics?

    So as to not waste this discussion, could I edit content in wikipedia page as it has nothing.

    Are these valid references?



    http://relativity.livingreviews.org/Articles/lrr-2008-5/ [Broken] see Sec 6.8 Dynamics: III. Group field theory



    [gr-qc/0607032] The group field theory approach to quantum gravity by D Oriti - 2006 -

    [0710.3276] Group field theory as the microscopic description of ... by D Oriti - 2007

    http://fqxi.org/data/documents/Oriti Azores Talk.pdf


    Linearized Group Field Theory and Power Counting Theorems

    Joseph Ben Geloun, Thomas Krajewski, Jacques Magnen, Vincent Rivasseau (Submitted on 18 Feb 2010)
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jul 14, 2010 #2


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    Every spin foam is a GFT.

    Spacetime as a Feynman diagram: the connection formulation
    Michael P. Reisenberger, Carlo Rovelli

    Group field is to spin foam as Boulatov-Ooguri is to Pozano-Regge:
    Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space
    R. De Pietri, L. Freidel, K. Krasnov, C. Rovelli
  4. Jul 14, 2010 #3
    how does that enlarge the thought content? every sf is a sf.

    what is gft?
  5. Jul 14, 2010 #4


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    "The fourth avenue starts from approaches to quantum gravity in which gravity is to emerge from a more fundamental theory based on abstract structures that, to begin with, have nothing to do with space-time geometry. Examples are matrix models for 2-dimensional gravity and their extension to 3-dimensions —the Boulatov model [16]— where the basic object is a field on a group manifold rather than a matrix. The Boulatov model was further generalized to a group field theory (GFT) tailored to 4-dimensional gravity [4, 17, 18]. The perturbative expansion of this GFT turned out be very closely related to the vertex expansions in SFMs."

    "There is a also a tension between SFMs and GFTs. Although fields in GFTs live on an abstract manifold constructed from a Lie group, as in familiar field theories the action has a free part and an interaction term. The interaction term has a coupling constant, , as coefficient. One can therefore carry out a Feynman expansion and express the partition function, propagators, etc, as a perturbation series in . If one sets = 1, the resulting series can be identified with the vertex expansion of SFMs. But if one adopts the viewpoint that the GFT is fundamental and regards gravity as an emergent phenomenon, one is led to allow to run under the renormalization group flow." [My emphasis]
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