Cosmological Constant in LQG Vertex Amplitude

@article{Han2011CosmologicalCI,
  title={Cosmological Constant in LQG Vertex Amplitude},
  author={Muxin Han},
  journal={Physical Review D},
  year={2011},
  volume={84},
  pages={064010}
}
  • Muxin Han
  • Published 11 May 2011
  • Mathematics
  • Physical Review D
A new q-deformation of the Euclidean EPRL/FK vertex amplitude is proposed by using the evaluation of the Vassiliev invariant associated with a 4-simplex graph (related to two copies of quantum SU(2) group at different roots of unity) embedded in a 3-sphere. We show that the large-j asymptotics of the q-deformed vertex amplitude gives the Regge action with a cosmological constant. In the end we also discuss its relation with a Chern-Simons theory on the boundary of 4-simplex. 

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References

SHOWING 1-10 OF 35 REFERENCES
Linking topological quantum field theory and nonperturbative quantum gravity
Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory in which the
Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude
The semiclassical limit of a four-simplex amplitude for a spin foam quantum gravity model with an Immirzi parameter is studied. If the boundary state represents a nondegenerate four-simplex geometry,
Spinfoams in the holomorphic representation
We study a holomorphic representation for spinfoams. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mourao-Thiemann coherent state transform. We derive the expression of the 4d
Invariants of 3-manifolds via link polynomials and quantum groups
The aim of this paper is to construct new topological invariants of compact oriented 3-manifolds and of framed links in such manifolds. Our invariant of (a link in) a closed oriented 3-manifold is a
Cosmological deformation of Lorentzian spin foam models
We study the quantum deformation of the Barrett?Crane Lorentzian spin foam model which is conjectured to be the discretization of the Lorentzian Plebanski model with positive cosmological constant
Three-dimensional gravity from the Turaev-Viro invariant.
TLDR
In the semiclassical continuum limit the Turaev-Viro invariant obtained recently defines a naturally regularized path integral {ital a} {ital la} Ponzano and Regge, in which a contribution from the cosmological term is effectively included.
Topological lattice models in four-dimensions
We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group G. When G=SU(2), the statistical weight is constructed from the 15j-symbol as well as the
...
1
2
3
4
...