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  Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators

Dittrich, B., Hellmann, F., & Kaminski, W. (2013). Holonomy Spin Foam Models: Boundary Hilbert spaces and Time Evolution Operators. Classical and quantum gravity, 30(8): 085005. doi:10.1088/0264-9381/30/8/085005.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-000E-9607-9 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0015-16F8-E
Genre: Journal Article

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1209.4539 (Preprint), 546KB
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 Creators:
Dittrich, Bianca1, Author              
Hellmann, Frank2, Author              
Kaminski, Wojciech, Author
Affiliations:
1Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_102878              
2Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Lattice, hep-lat
 Abstract: In this and the companion paper a novel holonomy formulation of so called Spin Foam models of lattice gauge gravity are explored. After giving a natural basis for the space of simplicity constraints we define a universal boundary Hilbert space, on which the imposition of different forms of the simplicity constraints can be studied. We detail under which conditions this Hilbert space can be mapped to a Hilbert space of projected spin networks or an ordinary spin network space. These considerations allow to derive the general form of the transfer operators which generates discrete time evolution. We will describe the transfer operators for some current models on the different boundary Hilbert spaces and highlight the role of the simplicity constraints determining the concrete form of the time evolution operators.

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 Dates: 2012-09-202013
 Publication Status: Published in print
 Pages: 51 pages, 18 figures
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1209.4539
DOI: 10.1088/0264-9381/30/8/085005
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Title: Classical and quantum gravity
Source Genre: Journal
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Publ. Info: Bristol, U.K. : Institute of Physics
Pages: - Volume / Issue: 30 (8) Sequence Number: 085005 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: /journals/resource/954925513480_1