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Schlagwörter:
General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Lattice, hep-lat,High Energy Physics - Theory, hep-th
Zusammenfassung:
A path integral measure for gravity should also preserve the fundamental
symmetry of general relativity, which is diffeomorphism symmetry. In previous
work, we argued that a successful implementation of this symmetry into discrete
quantum gravity models would imply discretization independence. We therefore
consider the requirement of triangulation independence for the measure in
(linearized) Regge calculus, which is a discrete model for quantum gravity,
appearing in the semi--classical limit of spin foam models. To this end we
develop a technique to evaluate the linearized Regge action associated to
Pachner moves in 3D and 4D and show that it has a simple, factorized structure.
We succeed in finding a local measure for 3D (linearized) Regge calculus that
leads to triangulation independence. This measure factor coincides with the
asymptotics of the Ponzano Regge Model, a 3D spin foam model for gravity. We
furthermore discuss to which extent one can find a triangulation independent
measure for 4D Regge calculus and how such a measure would be related to a
quantum model for 4D flat space. To this end, we also determine the dependence
of classical Regge calculus on the choice of triangulation in 3D and 4D.
