Group field theories for all loop quantum gravity

Sep 10, 2014
49 pages
Published in:
  • New J.Phys. 17 (2015) 2, 023042
  • Published: Feb 13, 2015
e-Print:
Report number:
  • AEI-2014-044

Citations per year

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Abstract: (IOP)
Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.
Note:
  • version published in New Journal of Physics
  • field theory: group
  • spin: foam
  • quantum gravity: loop space
  • simplex