Simple spin networks as Feynman graphs
Open accessAbstract
We show how spin networks can be described and evaluated as Feynman integrals over an internal space. This description can, in particular, be applied to the so-called simple SO(D) spin networks that are of importance for higher-dimensional generalizations of loop quantum gravity. As an illustration of the power of the new formalism, we use it to obtain the asymptotics of an amplitude for the D simplex and show that its oscillatory part is given by the Regge action.
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For any non-degenerate triangulation with finitely many simplices, the Lorentzian amplitude (113) is finite, with the integral over simple continuous representations of the Lorentz group converging absolutely.
“In fact, it was proven [105], using the results of [104], that, for any non-degenerate and finite (finite number of simplices) triangulation, the amplitude (113) is finite, in the sense that the integral over the simple continuous representations of the Lorentz group converges absolutely.”
From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [104]
In most interesting cases, the evaluation of these spin networks is finite, i.e. integrable, as proven in [104].
“Moreover, in most of the interesting cases the evaluation of these spin networks is finite, i.e. they are integrable, as was proven in [104].”
From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [104]
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- Authors
- Freidel, L., & Krasnov, K.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- Pennsylvania State University (US)
- ORCID
- Freidel, L.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 2000-04-01
- Volume
- 41
- Issue
- 4
- Pages
- 1681-1690
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2140632344
- Cited by
- 42
- References
- 6
- Citations by year
- 2022: 2 · 2016: 1 · 2012: 2
- FWCI
- 4.07
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Mathematical Physics (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 › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- spin networks, Feynman integrals, loop quantum gravity, higher-dimensional generalization, Regge calculus, Regge action, asymptotic analysis, internal space
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