Path integral representation of spin foam models of 4d gravity
Open accessAbstract
We give a unified description of all recent spin foam models introduced by Engle, Livine, Pereira and Rovelli (ELPR) and by Freidel and Krasnov (FK). We show that the FK models are, for all values of the Immirzi parameter γ, equivalent to path integrals of a discrete theory and we provide an explicit formula for the associated actions. We discuss the relation between the FK and ELPR models and also study the corresponding boundary states. For general Immirzi parameter, these are given by Alexandrov's and Livine's SO(4) projected states. For 0 ⩽ γ < 1, the states can be restricted to SU(2) spin networks.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The boundary amplitude of a coherent spin network |j, Φ(n)> admits an integral representation over five copies of SU(2)×SU(2) with action S = S+ + S-.
“The boundary amplitude of a coherent spin network |j, Φ( n) admits an integral representation [32,34,35].”
From LQG propagator from the new spin foams (2009) · cites this paper as [32]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Quantum Theory of Angular Momentum
Варшалович, Д. А., Moskalev, A. N., & Khersonskii, V. K. (1988) · WORLD SCIENTIFIC eBooks · doi:10.1142/0270 · Cited by 3,835 · see citing works
Rovelli, C. (2004) · doi:10.1017/cbo9780511755804 · Cited by 2,240 · see citing works
LQG vertex with finite Immirzi parameter
Engle, J., Livine, E., Pereira, R., & Rovelli, C. (2008) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2008.02.018 · Cited by 584 · see citing works
Spin foam models for quantum gravity
Perez, A. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/6/202 · Cited by 532 · see citing works
Relativistic spin networks and quantum gravity
Barrett, J. W., & Crane, L. (1998) · Journal of Mathematical Physics · doi:10.1063/1.532254 · Cited by 404 · see citing works
New spinfoam vertex for quantum gravity
Livine, E. R., & Speziale, S. (2007) · Physical Review D · doi:10.1103/physrevd.76.084028 · Cited by 401 · see citing works
Baez, J. C. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/7/004 · Cited by 381 · see citing works
Group Field Theory: An Overview
Freidel, L. (2005) · International Journal of Theoretical Physics · doi:10.1007/s10773-005-8894-1 · Cited by 378 · see citing works
Self-citationLoop-Quantum-Gravity Vertex Amplitude
Engle, J., Pereira, R., & Rovelli, C. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.161301 · Cited by 335 · see citing works
Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory
Freidel, L., & Livine, E. R. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/6/012 · Cited by 266 · see citing works
Self-citationBarrett–Crane model from a Boulatov–Ooguri field theory over a homogeneous space
De Pietri, R., Freidel, L., Krasnov, K., & Rovelli, C. (2000) · Nuclear Physics B · doi:10.1016/s0550-3213(00)00005-5 · Cited by 244 · see citing works
Self-citationFlipped spinfoam vertex and loop gravity
Engle, J., Pereira, R., & Rovelli, C. (2008) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2008.02.002 · Cited by 241 · see citing works
Ponzano–Regge model revisited: I. Gauge fixing, observables and interacting spinning particles
Freidel, L., & Louapre, D. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/24/002 · Cited by 218 · see citing works
Self-citationSpacetime as a Feynman diagram: the connection formulation
Reisenberger, M. P., & Rovelli, C. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/1/308 · Cited by 202 · see citing works
Spin foam models and the classical action principle
Freidel, L., & Krasnov, K. (1998) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1998.v2.n6.a1 · Cited by 195 · see citing works
Self-citationThree-dimensional loop quantum gravity: physical scalar product and spin-foam models
Noui, K., & Perez, A. (2005) · Classical and Quantum Gravity · doi:10.1088/0264-9381/22/9/017 · Cited by 181 · see citing works
A “general boundary” formulation for quantum mechanics and quantum gravity
Oeckl, R. (2003) · Physics Letters B · doi:10.1016/j.physletb.2003.08.043 · Cited by 167 · see citing works
Alexandrov, S., & Livine, E. R. (2003) · Physical Review D · doi:10.1103/physrevd.67.044009 · Cited by 141 · see citing works
<i>SO</i> (4, <i>C</i> )-covariant Ashtekar-Barbero gravity and the Immirzi parameter
Alexandrov, S. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/20/307 · Cited by 112 · see citing works
Particle Scattering in Loop Quantum Gravity
Modesto, L., & Rovelli, C. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.191301 · Cited by 93 · see citing works
Choice of connection in loop quantum gravity
Alexandrov, S. (2001) · Physical Review D · doi:10.1103/physrevd.65.024011 · Cited by 80 · see citing works
Projected spin networks for Lorentz connection: linking spin foams and loop gravity
Livine, E. R. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/21/316 · Cited by 77 · see citing works
Lorentzian loop quantum gravity vertex amplitude
Roberto Pereira, B. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/8/085013 · Cited by 77 · see citing works
Area spectrum in Lorentz covariant loop gravity
Alexandrov, S., & Vassilevich, D. (2001) · Physical Review D · doi:10.1103/physrevd.64.044023 · Cited by 68 · see citing works
The dual of pure non-Abelian lattice gauge theory as a spin foam model
Oeckl, R., & Pfeiffer, H. (2001) · Nuclear Physics B · doi:10.1016/s0550-3213(00)00770-7 · Cited by 46 · see citing works
Livine, R. E., & Oriti, D. (2002) · Physical Review D · doi:10.1103/physrevd.65.044025 · Cited by 46 · see citing works
Hilbert space structure of covariant loop quantum gravity
Alexandrov, S. (2002) · Physical Review D · doi:10.1103/physrevd.66.024028 · Cited by 42 · see citing works
Coherent states, constraint classes and area operators in the new spin-foam models
Engle, J., & Roberto Pereira, B. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/10/105010 · Cited by 32 · see citing works
Flagged first, then by citations
Research works printed but not linked: 9
- Hamber H W 2007 Discrete and continuum quantum gravity arXiv:0704.2895 · arXiv
- Ambjorn J, Jurkiewicz J and Loll R 2006 Quantum gravity, or the art of building spacetime arXiv:hep-th/0604212 · arXiv
- Freidel L and Louapre D 2004 Ponzano-Regge model revisited: II. Equivalence with Chern-Simons arXiv:gr-qc/0410141 · arXiv
- Freidel L and Krasnov K 2007 A new spin foam model for 4D gravity arXiv:0708.1595 · arXiv
- Livine E R and Speziale S 2007 Consistently solving the simplicity constraints for spinfoam quantum gravity arXiv:0708.1915 · arXiv
- Reisenberger M P 1997 A lattice worldsheet sum for 4D Euclidean general relativity arXiv:gr-qc/9711052 · arXiv
- Oeckl R 2003 The general boundary approach to quantum gravity arXiv:gr-qc/0312081 · arXiv
- Bianchi E, Modesto L, Rovelli C and Speziale S 2006 Graviton propagator in loop quantum gravity arXiv:gr-qc/0604044 · arXiv
- Conrady F 2006 Analytic derivation of gluons and monopoles from SU(2) lattice Yang-Mills theory: II. Spin foam representation arXiv:hep-th/0610237 · arXiv
Cited by
Sorted by citations
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
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
Barrett, J. W., Dowdall, R. J., Fairbairn, W. J., Hellmann, F., & Pereira, R. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/16/165009 · Cited by 247 · see citing works
LQG propagator from the new spin foams
Bianchi, E., Magliaro, E., & Perini, C. (2009) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2009.07.016 · Cited by 126 · see citing works
“1 Integral formula for the amplitude of a coherent spin network The boundary amplitude of a coherent spin network |j,Φ(~n)〉 admits an integral representation [32, 34],[35].”
BackgroundMethodInfluential(Broken) Gauge symmetries and constraints in Regge calculus
Bahr, B., & Dittrich, B. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/22/225011 · Cited by 94 · see citing works
Lorentz covariance of loop quantum gravity
Rovelli, C., & Speziale, S. (2011) · Physical Review D · doi:10.1103/physrevd.83.104029 · Cited by 84 · see citing works
The Euclidean three-point function in loop and perturbative gravity
Rovelli, C., & Zhang, M. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/17/175010 · Cited by 31 · see citing works
- Authors
- Conrady, F., & Freidel, L.
- Affiliations
- Perimeter Institute (CA)
- ORCID
- Freidel, Laurent
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2008-12-02
- Volume
- 25
- Issue
- 24
- Pages
- 245010
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1984186082
- Cited by
- 98
- References
- 28
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 1 · 2023: 2 · 2022: 2 · 2020: 1 · 2019: 1 · 2018: 2 · 2017: 3 · 2016: 3 · 2014: 5 · 2013: 11 · 2012: 13
- FWCI
- 13.14
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.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 › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- spin foam models, path integral representation, four-dimensional gravity, Immirzi parameter, discrete gravity, boundary states, quantum gravity
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
