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. 
View PDF on arXiv
56 Citations
Highly Influential Citations
2
Background Citations
17
Methods Citations
7
Results Citations
1

Figures from this paper

56 Citations

Citation Type

Citation Type

SL(2,C) Chern–Simons theory, a non-planar graph operator, and 4D quantum gravity with a cosmological constant: Semiclassical geometry
Renormalization in symmetry restricted spin foam models with curvature
We study the renormalization group flow of the Euclidean Engle-Pereira-Rovelli-Livine and Freidel-Krasnov (EPRL-FK) spin foam model in its asymptotic limit. The vertex amplitude is deformed to…
Deformation of the Engle-Livine-Pereira-Rovelli spin foam model by a cosmological constant
In this article, we consider an ad-hoc deformation of the EPRL model for quantum gravity by a cosmological constant term. This sort of deformation has been first introduced by Han for the case of the…
On the dynamical emergence of SUq(2) from the regularization of 2 + 1D gravity with cosmological constant
The quantization of the reduced phase-space of the Einstein-Hilbert action for gravity in 2 + 1D has been shown to bring to the emergence, at the quantum level, of a topological quantum field theory…
Anyonic statistics and large horizon diffeomorphisms for loop quantum gravity black holes
We investigate the role played by large diffeomorphisms of quantum Isolated Horizons for the statistics of LQG Black Holes by means of their relation to the braid group. To this aim the symmetries of…
Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
We study the renormalization group flow of the Euclidean Engle-Pereira-Rovelli-Livine and Freidel-Krasnov (EPRL-FK) spin foam model in the large-$j$ limit. The vertex amplitude is deformed to include…
Numerical analysis of the self-energy in covariant LQG
We study numerically the first order radiative corrections to the self-energy, in covariant loop quantum gravity. We employ the recently developed sl2cfoam-next spinfoam amplitudes library, and some…
Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
We calculate the most divergent contribution to non-degenerate sectorof the self-energy (or “melonic”) graph in the context of the Lorentzian EPRL-FK Spin Foam model of Quantum Gravity. We find that…
On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity
Spin Foam and Loop approaches to Quantum Gravity reformulate Einstein's theory of relativity in terms of connection variables. The metric properties are encoded in face bivectors/conjugate fluxes…
Discrete Symmetries in Covariant LQG
We study time-reversal and parity ---on the physical manifold and in internal space--- in covariant loop gravity. We consider a minor modification of the Holst action which makes it transform…
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 35 REFERENCES
LQG vertex with finite Immirzi parameter
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…
Quantum deformation of quantum gravity
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.
State sum invariants of 3 manifolds and quantum 6j symbols
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
...