Cosmological constant in loop quantum gravity vertex amplitude (original) (raw)
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Abstract
A new q deformation of the Euclidean EPRL/FK (Engle-Pereira-Rovelli-Livine/Freidel-Krasnov) 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.
Publication:
Physical Review D
Pub Date:
September 2011
DOI:
arXiv:
Bibcode:
Keywords:
- 04.60.Pp;
- 02.20.Uw;
- Loop quantum gravity quantum geometry spin foams;
- Quantum groups;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory;
- Mathematical Physics
E-Print:
6 pages, 5 figures, result and presentation improved