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  Path integral measure and triangulation independence in discrete gravity

Dittrich, B., & Steinhaus, S. (2012). Path integral measure and triangulation independence in discrete gravity. Physical Review D, 85(4): 044032. doi:10.1103/PhysRevD.85.044032.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-3112-B Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-7BD2-1
Genre: Journal Article

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1110.6866 (Preprint), 424KB
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 Creators:
Dittrich, Bianca1, Author              
Steinhaus, Sebastian2, Author              
Affiliations:
1Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_102878              
2Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_persistent22              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Lattice, hep-lat,High Energy Physics - Theory, hep-th
 Abstract: 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.

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 Dates: 2011-10-312012
 Publication Status: Published in print
 Pages: 36 pages, 7 figures
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1110.6866
URI: http://arxiv.org/abs/1110.6866
DOI: 10.1103/PhysRevD.85.044032
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : American Physical Society
Pages: - Volume / Issue: 85 (4) Sequence Number: 044032 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: /journals/resource/111088197762258