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  Perfect discretization of reparametrization invariant path integrals

Bahr, B., Dittrich, B., & Steinhaus, S. (2011). Perfect discretization of reparametrization invariant path integrals. Physical Review D, 83(10): 105026. doi:10.1103/PhysRevD.83.105026.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0010-9756-7 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0010-9759-1
Genre: Journal Article

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1101.4775 (Preprint), 321KB
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 Creators:
Bahr, Benjamin1, Author              
Dittrich, Bianca1, Author              
Steinhaus, Sebastian2, Author              
Affiliations:
1Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:102878              
2Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:persistent22              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Lattice, hep-lat
 Abstract: To obtain a well defined path integral one often employs discretizations. In the case of gravity and reparametrization invariant systems, the latter of which we consider here as a toy example, discretizations generically break diffeomorphism and reparametrization symmetry, respectively. This has severe implications, as these symmetries determine the dynamics of the corresponding system. Indeed we will show that a discretized path integral with reparametrization invariance is necessarily also discretization independent and therefore uniquely determined by the corresponding continuum quantum mechanical propagator. We use this insight to develop an iterative method for constructing such a discretized path integral, akin to a Wilsonian RG flow. This allows us to address the problem of discretization ambiguities and of an anomaly--free path integral measure for such systems. The latter is needed to obtain a path integral, that can act as a projector onto the physical states, satisfying the quantum constraints. We will comment on implications for discrete quantum gravity models, such as spin foams.

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 Dates: 2011-01-252011
 Publication Status: Published in print
 Pages: 22+8 pages
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1101.4775
DOI: 10.1103/PhysRevD.83.105026
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Title: Physical Review D
  Other : Phys. Rev. D.
Source Genre: Journal
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Publ. Info: Lancaster, Pa. : Published for the American Physical Society by the American Institute of Physics
Pages: - Volume / Issue: 83 (10) Sequence Number: 105026 Start / End Page: - Identifier: ISSN: 0556-2821
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/111088197762258