Volume 81, Number 5, March 2008
|Number of page(s)||6|
|Published online||13 February 2008|
Solving the simplicity constraints for spinfoam quantum gravity
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
Accepted: 14 January 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 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.
PACS: 04.60.Pp – Loop quantum gravity, quantum geometry, spin foams
© EPLA, 2008
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