| Issue |
EPL
Volume 81, Number 5, March 2008
|
|
|---|---|---|
| Article Number | 50004 | |
| Number of page(s) | 6 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/81/50004 | |
| Published online | 13 February 2008 | |
Solving the simplicity constraints for spinfoam quantum gravity
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
Corresponding authors: etera.livine@ens-lyon.fr sspeziale@perimeterinstitute.ca
Received:
21
November
2007
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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