Spinfoam 2D quantum gravity and discrete bundles
Open accessAbstract
In 4 dimensions, general relativity can be formulated as a constrained $BF$ theory; we show that the same is true in 2 dimensions. We describe a spinfoam quantization of this constrained BF-formulation of 2d riemannian general relativity, obtained using the Barrett-Crane technique of imposing the constraint as a restriction on the representations summed over. We obtain the expected partition function, thus providing support for the viability of the technique. The result requires the nontrivial topology of the bundle where the gravitational connection is defined, to be taken into account. For this purpose, we study the definition of a principal bundle over a simplicial base space. The model sheds light also on several other features of spinfoam quantum gravity: the reality of the partition function; the geometrical interpretation of the Newton constant, and the issue of possible finiteness of the partition function of quantum general relativity.
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Two-dimensional BF theory is related to usual two-dimensional gravity through constraints in a way similar to the four-dimensional case.
“on the other hand, it is related to usual 2D gravity via constraints in a way similar to the one exploited in four dimensions (see Section 7).”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [295]
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The Spin-Foam Approach to Quantum Gravity
Perez, A. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-3 · Cited by 677 · see citing works
- Authors
- Oriti, D., Rovelli, C., & Speziale, S.
- ORCID
- Oriti, Daniele
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2004-12-04
- Volume
- 22
- Issue
- 1
- Pages
- 85-108
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1968042125
- Cited by
- 9
- References
- 20
- Citations by year
- 2023: 1 · 2019: 1 · 2016: 1 · 2013: 1 · 2012: 2
- FWCI
- 0.23
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- two-dimensional quantum gravity, Barrett-Crane model, principal bundles, partition function, Newton constant
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