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  Operator Spin Foam Models

Bahr, B., Hellmann, F., Kamiński, W., Kisielowski, M., & Lewandowski, J. (2011). Operator Spin Foam Models. Classical and quantum gravity, 28(10): 105003. doi:10.1088/0264-9381/28/10/105003.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-CE76-B Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-CE78-7
Genre: Journal Article

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1010.4787 (Preprint), 926KB
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 Creators:
Bahr, Benjamin1, Author              
Hellmann, Frank, Author
Kamiński, Wojciech, Author
Kisielowski, Marcin, Author
Lewandowski, Jerzy, Author
Affiliations:
1Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:102878              

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Free keywords: General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
 Abstract: The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as the main tool. An equivalence relation we impose in the set of the operator spin foams allows to split the faces and the edges of the foams. The consistency with that relation requires introduction of the (familiar for the BF theory) face amplitude. The operator spin foam models are defined quite generally. Imposing a maximal symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with demanding consistency with splitting the edges, determines a complete characterization of a general natural model. It can be obtained by applying arbitrary (quantum) constraints on an arbitrary BF spin foam model. In particular, imposing suitable constraints on Spin(4) BF spin foam model is exactly the way we tend to view 4d quantum gravity, starting with the BC model and continuing with the EPRL or FK models. That makes our framework directly applicable to those models. Specifically, our operator spin foam framework can be translated into the language of spin foams and partition functions. We discuss the examples: BF spin foam model, the BC model, and the model obtained by application of our framework to the EPRL intertwiners.

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 Dates: 2010-10-222011
 Publication Status: Published in print
 Pages: 19 pages, 11 figures, RevTex4.1
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1010.4787
URI: http://arxiv.org/abs/1010.4787
DOI: 10.1088/0264-9381/28/10/105003
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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: 28 (10) Sequence Number: 105003 Start / End Page: - Identifier: ISSN: 0264-9381
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/954925513480_1