Solving the simplicity constraints for spinfoam quantum gravityE. R. Livine1 and S. Speziale2
1 Laboratoire de Physique, ENS Lyon, CNRS UMR 5672 - 46 Allée d'Italie, 69007 Lyon, France
2 Perimeter Institute - 31 Caroline St North, Waterloo, ON N2L 2Y5, Canada
received 21 November 2007; accepted in final form 14 January 2008; published March 2008
published online 13 February 2008
General relativity can be written as topological BF theory plus a set of second-class constraints. Classically the constraints provide the geometric interpretation of the B variables and reduce BF to general relativity. In the quantum theory these constraints do not commute and thus cannot be imposed strongly. We use SU(2) coherent states to develop a notion of semiclassical states for the quantum geometry which allows to implement them weakly, i.e. on average with minimal uncertainty. Using the spinfoam formalism, this leads to a background independent regularized path integral for quantum gravity whose variables have a transparent geometric interpretation.
04.60.Pp - Loop quantum gravity, quantum geometry, spin foams.
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