# 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} }

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.

## 56 Citations

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## References

SHOWING 1-10 OF 35 REFERENCES

Linking topological quantum field theory and nonperturbative quantum gravity

- Mathematics
- 1995

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

- Physics
- 2009

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

- Mathematics
- 2010

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

- Mathematics
- 1991

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

- Physics
- 2003

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.

- PhysicsPhysical review letters
- 1992

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

- Mathematics
- 1992

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…