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Abstract: 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 anglesand includes the Immirzi parameter. In addition, a measure is inserted toensure a consistent gluing of simplices, so that the amplitude is dominated byconfigurations which satisfy the parallel transport relations. We explicitlycompute the path integral as a sum over spin foams for a generic measure. TheFreidel-Krasnov and Engle-Pereira-Rovelli models correspond to a special choiceof 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 withrespect to area variations requires spacetime geometry to be flat.



Autor: Valentin Bonzom

Fuente: https://arxiv.org/







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