Cosmological constant in loop quantum gravity vertex amplitude
Abstract
A new q deformation of the Euclidean EPRL/FK (EnglePereiraRovelliLivine/FreidelKrasnov) vertex amplitude is proposed by using the evaluation of the Vassiliev invariant associated with a 4simplex graph [related to two copies of quantum SU(2) group at different roots of unity] embedded in a 3sphere. We show that the largej asymptotics of the qdeformed vertex amplitude gives the Regge action with a cosmological constant. In the end we also discuss its relation with a ChernSimons theory on the boundary of 4simplex.
 Publication:

Physical Review D
 Pub Date:
 September 2011
 DOI:
 10.1103/PhysRevD.84.064010
 arXiv:
 arXiv:1105.2212
 Bibcode:
 2011PhRvD..84f4010H
 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
 EPrint:
 6 pages, 5 figures, result and presentation improved