Diffeomorphisms and spin foam models
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Freidel and Louapre further show that the symmetry can be gauge-fixed, leading to a sum over a restricted and considerably simplified class of "collapsed" triangulations.
“Freidel and Louapre further show that the symmetry can instead be gauge-fixed, leading to a sum over a restricted and considerably simplified class of “collapsed” triangulations.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [131]
The Discussion (p. 13) says gauge fixing the translational symmetry amounts to computing the partition function on a collapsed triangulation. The Gauge fixing procedure (pp. 11–12) explains how collapsing edges along a maximal tree produces such a triangulation. Our copy does not describe a sum over a class of collapsed triangulations; it describes a partition function on a collapsed triangulation. (LLM, conf=0.84)
Experimental — accuracy not yet measuredFreidel and Louapre show that a residual piece of the diffeomorphism symmetry has not been factored out of the Ponzano-Regge action; because of this symmetry, the sum (67) overcounts physical configurations, and the regulator Λ(L) is the remaining gauge volume.
“This mystery may have recently been solved by Freidel and Louapre [131], who show that a residual piece of the diffeomorphism symmetry has not been factored out of the Ponzano-Regge action. Because of this symmetry, the sum (67) overcounts physical configurations, and the regulator Λ(L) is simply the remaining gauge volume.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [131]
The Ponzano-Regge model is well defined when natural regularizations are used.
“We will see in Part IV that natural regularizations are available and that the model is well defined [67, 281, 186].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [186]
Divergences in the partition function arise from infinite volume factors associated with the topological gauge freedom.
“Divergences occur due to infinite volume factors corresponding to the topological gauge freedom (225) (see [186]).”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [186]
In 3D gravity, bubble divergences are directly linked to the infinite volume of the gauge orbits generated by the curvature constraint.
“This is illustrated precisely in the simplest scenario of 3D gravity, where it is well known that bubble divergences are directly linked to the infinite volume of the gauge orbits generated by the curvature constraint [186].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [186]
Gauge-fixing conditions generally exist in spin-foam models and are used to regularize the vertex amplitudes of the Lorentzian models.
“These conditions generally exist in spin-foam models and are used to regularize the vertex amplitudes of the Lorentzian models (we have illustrated this at the end of Section 8.3; for a general treatment see [186]).”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [186]
The sum over spins in (247) is typically divergent, so discretization independence is only formal without a suitable regularization.
“The sum over spins in (247) is typically divergent, as indicated by the previous equation. Divergences occur due to infinite volume factors corresponding to the topological gauge freedom (225) (see [186]).30 The factor τ in (248) represents such a volume factor. It can also be interpreted as a δ(0) coming from the existence of a redundant delta function in (242).”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [186]
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References 21 · Cited by 155
Research works printed but not linked: 1
- [16]G. T. Horowitz, Topology change in general relativity , 6th Marcel Grossman meeting, Kyoto, Japan (1991), hep-th/9109030 . · arXiv
- Authors
- Freidel, L., & Louapre, D.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- Corresponding author
- Freidel, Laurent
- Louapre, David
- Venue
- Nuclear Physics B
- Publisher
- Elsevier BV
- Published
- 2003-07
- Volume
- 662
- Issue
- 1-2
- Pages
- 279-298
- ISSN
- 0550-3213 (ISSN-L)
- OpenAlex
- W1976604005
- Cited by
- 155
- References
- 21
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 4 · 2023: 3 · 2022: 2 · 2021: 1 · 2020: 5 · 2019: 2 · 2018: 5 · 2017: 3 · 2016: 6 · 2015: 8 · 2014: 16 · 2013: 12 · 2012: 15
- FWCI
- 7.48
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Nuclear Physics B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (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 › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Keywords
- diffeomorphism invariance, spin foam models, state sum models, Ponzano-Regge model, renormalization, gauge fixing, residual symmetry, divergence
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