Spin foam models for quantum gravity from lattice path integrals
- Centre de Physique Theorique, CNRS-UMR 6207, Luminy Case 907, 13288 Marseille (France) and Laboratoire de Physique, ENS Lyon, CNRS-UMR 5672, 46 Allee d'Italie, 69007 Lyon (France)
Spin foam models for quantum gravity are derived from lattice path integrals. The setting involves variables from both lattice BF theory and Regge calculus. The action consists in a Regge action, which depends on areas, dihedral angles and includes the Immirzi parameter. In addition, a measure is inserted to ensure a consistent gluing of simplices, so that the amplitude is dominated by configurations that satisfy the parallel transport relations. We explicitly compute the path integral as a sum over spin foams for a generic measure. The Freidel-Krasnov and Engle-Pereira-Rovelli models correspond to a special choice of gluing. In this case, the equations of motion describe genuine geometries, where the constraints of area-angle Regge calculus are satisfied. Furthermore, the Immirzi parameter drops out of the on-shell action, and stationarity with respect to area variations requires spacetime geometry to be flat.
- OSTI ID:
- 21322741
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 80, Issue 6; Other Information: DOI: 10.1103/PhysRevD.80.064028; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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