The DOI matches its Crossref record; 268 of the 268 references it cites were found in a registry or an index.
Background independent quantum gravity: a status report
Open accessAbstract
The goal of this review is to present an introduction to loop quantum gravity—a background-independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of geometry. Our presentation is pedagogical. Thus, in addition to providing a bird's eye view of the present status of the subject, the review should also serve as a vehicle to enter the field and explore it in detail. To aid non-experts, very little is assumed beyond elements of general relativity, gauge theories and quantum field theory. While the review is essentially self-contained, the emphasis is on communicating the underlying ideas and the significance of results rather than on presenting systematic derivations and detailed proofs. (These can be found in the listed references.) The subject can be approached in different ways. We have chosen one which is deeply rooted in well-established physics and also has sufficient mathematical precision to ensure that there are no hidden infinities. In order to keep the review to a reasonable size, and to avoid overwhelming non-experts, we have had to leave out several interesting topics, results and viewpoints; this is meant to be an introduction to the subject rather than an exhaustive review of it.
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In the citing paper
“Indeed, although spinfoam models have been derived in a number of different manners [6, 7, 8, 21], most derivations involve peculiar procedures or intuitive and ad hoc steps.”
From Flipped spinfoam vertex and loop gravity (2008) · cites this paper as [8]
Experimental — accuracy not yet measuredThe check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“The original model of [2, 3] and the variant pointed out in [11] appear as limiting γ → 0 and γ → ∞ cases, respectively.”
From LQG vertex with finite Immirzi parameter (2008) · cites this paper as [11]
Experimental — accuracy not yet measuredIn the citing paper
“LQG is a proposal for the implementation of the quantization program established in the 1960s by Dirac, Wheeler, and DeWitt, among others (for recent reviews see [35, 356, 323]).”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [35]
In the citing paper
“One of the celebrated results of loop quantum gravity ͑LQG͒ is the discreteness of the spectrum of geometrical operators such as length, area, and volume operators.”
From Are the spectra of geometrical operators in loop quantum gravity really discrete? (2009) · cites this paper as [2]
In the citing paper
“All these models ([2, 3, 11, 12],) are defined by the same vertex, namely the square of the SU (2) Wigner 15 j symbol; they differ for the class of boundary states considered and their measure in the spinfoam sum.”
From LQG vertex with finite Immirzi parameter (2008) · cites this paper as [11]
In the citing paper
“In [11], it was shown that these constraints can equivalently be solved using a different technique, based on coherent states, yielding the same result.”
From LQG vertex with finite Immirzi parameter (2008) · cites this paper as [11]
In the citing paper
“The best studied model in the 4d euclidean context is the Barrett-Crane (BC) theory [8], which is based on the vertex amplitude introduced by Barrett and Crane [7].”
From Flipped spinfoam vertex and loop gravity (2008) · cites this paper as [8]
In the citing paper
“The state ω 0 is well known, and is extensively used in the loop quantization [22, 6].”
From Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras (2006) · cites this paper as [6]
In the citing paper
“For example, the symmetry group provides a new, elegant version of a map Cyl → Cyl ∗ (the algebraic dual) which averages with respect to the (allowed) diffeomorphisms of Σ.”
From Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras (2006) · cites this paper as [6]
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Self-citationLoop quantum cosmology: IV. Discrete time evolution
Martin Bojowald, A. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/6/308 · Cited by 124
Volume Operator in Discretized Quantum Gravity
Loll, R. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.3048 · Cited by 124
Dynamical Initial Conditions in Quantum Cosmology
Martin Bojowald, A. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.121301 · Cited by 117
Canonical Quantum GravityPreprint
Kuchař, K. V. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9304012 · Cited by 117
Coherent State Transforms for Spaces of Connections
Ashtekar, A., Lewandowski, J., Marolf, D. M., Mourão, J. M., & Thiemann, T. (1996) · Journal of Functional Analysis · doi:10.1006/jfan.1996.0018 · Cited by 115
Self-citationA lattice worldsheet sum for 4-d Euclidean general relativityPreprint
Reisenberger, M. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9711052 · Cited by 113
Homogeneous loop quantum cosmology: the role of the spin connection
Martin Bojowald, A., Date, G., & Vandersloot, K. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/4/034 · Cited by 113
Lewandowski, J. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1/010 · Cited by 112
Self-citationThiemann, T. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/17/301 · Cited by 112
Gauge field theory coherent states (GCS) III: Ehrenfest theoremsPreprint
Thiemann, T., & Winkler, O. (2001) · Cited by 112
Gibbons, G. W. (1995) · Contemporary Physics · doi:10.1080/00107519508222175 · Cited by 109
Specialization of Ashtekar's Formalism to Bianchi Cosmology
Kodama, H. (1988) · Progress of Theoretical Physics · doi:10.1143/ptp.80.1024 · Cited by 109
On Quantum Statistical Mechanics of a Schwarzschild Black Hole
Krasnov, K. V. (1998) · General Relativity and Gravitation · doi:10.1023/a:1018820916342 · Cited by 106
Relation between polymer and Fock excitations
Ashtekar, A., & Lewandowski, J. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/18/102 · Cited by 105
Self-citationLoop quantum cosmology, boundary proposals, and inflation
Martin Bojowald, A., & Vandersloot, K. (2003) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.67.124023 · Cited by 105
Polymer and Fock representations for a scalar field
Ashtekar, A., Lewandowski, J., & Sahlmann, H. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/1/103 · Cited by 104
Self-citationSpin foam model for Lorentzian general relativity
Pérez, A., & Carlo Rovelli, C. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.63.041501 · Cited by 102
Structural properties of amorphous hydrogenated carbon. III. NMR investigations
Jäger, C., Gottwald, J., Spiess, H. W., et al. (1994) · Physical review. B, Condensed matter · doi:10.1103/physrevb.50.846 · Cited by 101
New variables for canonical supergravity
Ted Jacobson, A. (1988) · Classical and Quantum Gravity · doi:10.1088/0264-9381/5/6/012 · Cited by 101
Complexifier Coherent States for Quantum General Relativity
Thiemann, T. (2006) · Max Planck Institute for Plasma Physics · Cited by 100
Multipole Moments of Isolated Horizons
Ashtekar, A., Engle, J., Pawlowski, T., & Broeck, C. V. D. (2004) · CERN Document Server (European Organization for Nuclear Research) · Cited by 99
Self-citationAshtekar, A., Carlo Rovelli, C., & Smolin, L. (1991) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.44.1740 · Cited by 97
Self-citationThe complete spectrum of the area from recoupling theory in loop quantum gravity
Frittelli, S., Lehner, L., & Rovelli, C. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/11/008 · Cited by 95
Gambini, R., Porto, R. A., & Pullin, J. A. (2004) · New Journal of Physics · doi:10.1088/1367-2630/6/1/045 · Cited by 95
Spin networks in nonperturbative quantum gravity
Baez, J. C. (1996) · Proceedings of symposia in applied mathematics · doi:10.1090/psapm/051/1372769 · Cited by 92
Spectrum of the volume operator in quantum gravity
Loll, R. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(95)00627-3 · Cited by 90
On the Generality of Refined Algebraic Quantization
Giulini, D., & Marolf, D. M. (1998) · CERN Document Server (European Organization for Nuclear Research) · Cited by 88
Stochastic path integrals and open quantum systems
Strunz, W. T. (1996) · Physical Review A · doi:10.1103/physreva.54.2664 · Cited by 87
Einstein A and B coefficients for a black hole
Bekenstein, J. D., & Meisels, A. (1977) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.15.2775 · Cited by 86
Spacetime states and covariant quantum theory
Reisenberger, M., & Carlo Rovelli, C. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.65.125016 · Cited by 85
Towards the QFT on Curved Spacetime Limit of QGR. I: A General SchemePreprint
Sahlmann, H., & Thiemann, T. (2002) · Cited by 85
Loop quantum cosmology: III. Wheeler-DeWitt operators
Bojowald, M. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/6/307 · Cited by 83
Is Barbero's Hamiltonian formulation a gauge theory of Lorentzian gravity?
Samuel, J. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/20/101 · Cited by 83
Black holes and relativistic stars
Wald, R. M. (1998) · CERN Document Server (European Organization for Nuclear Research) · Cited by 82
The complete spectrum of the area from recoupling theory in loop quantum gravity
Frittelli, S., Lehner, L., & Carlo Rovelli, C. (1996) · CERN Document Server (European Organization for Nuclear Research) · Cited by 82
Photons from quantized electric flux representations
Varadarajan, M. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.64.104003 · Cited by 81
Nonperturbative summation over 3D discrete topologies
Freidel, L., & Louapre, D. (2003) · Physical Review D · doi:10.1103/physrevd.68.104004 · Cited by 80
Polymer and Fock representations for a Scalar fieldPreprint
Ashtekar, A., Lewandowski, J., & Sahlmann, H. (2002) · Cited by 80
Self-citationSpacetimes admitting isolated horizons
Lewandowski, J. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/4/101 · Cited by 79
Self-citationLoop constraints: A habitat and their algebra
Lewandowski, J., & Marolf, D. (1998) · MPG.PuRe (Max Planck Society) · Cited by 79
Self-citationAn algebraic extension of Dirac quantization: Examples
Ashtekar, A., & Tate, R. S. (1994) · Journal of Mathematical Physics · doi:10.1063/1.530684 · Cited by 77
Self-citationON THE CONSISTENCY OF THE CONSTRAINT ALGEBRA IN SPIN NETWORK QUANTUM GRAVITY
GAMBINI, R., LEWANDOWSKI, J., MAROLF, D., & PULLIN, J. (1998) · International Journal of Modern Physics D · doi:10.1142/s0218271898000103 · Cited by 77
Self-citationLOOP CONSTRAINTS: A HABITAT AND THEIR ALGEBRA
LEWANDOWSKI, J., & MAROLF, D. (1998) · International Journal of Modern Physics D · doi:10.1142/s0218271898000231 · Cited by 76
Self-citationQuantum Suppression of the Generic Chaotic Behavior Close to Cosmological Singularities
Martin Bojowald, A., & Date, G. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.071302 · Cited by 75
Fock representations from U(1) holonomy algebras
Varadarajan, M. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.104001 · Cited by 74
Canonical Quantization of General Relativity in Discrete Space-Times
Gambini, R., & Pullin, J. A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.021301 · Cited by 73
Finiteness of a spinfoam model for Euclidean quantum general relativity
Perez, A. (2001) · Nuclear Physics B · doi:10.1016/s0550-3213(01)00014-1 · Cited by 73
On relativistic spin network vertices
Reisenberger, M. P. (1999) · Journal of Mathematical Physics · doi:10.1063/1.532850 · Cited by 72
Operators for quantized directions
Major, S. (1999) · Classical and Quantum Gravity · doi:10.1088/0264-9381/16/12/307 · Cited by 71
Functional Integration on Spaces of Connections
Baez, J. C., & Sawin, S. (1997) · Journal of Functional Analysis · doi:10.1006/jfan.1997.3108 · Cited by 69
Physics with nonperturbative quantum gravity: Radiation from a quantum black hole
Barreira, M., Mauro Carfora, B., & Carlo Rovelli, C. (1996) · General Relativity and Gravitation · doi:10.1007/bf02109521 · Cited by 66
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On the consistency of the constraint algebra in spin network quantum gravity
Gambini, R., Lewandowski, J., Marolf, D. M., & Pullin, J. A. (1997) · Civil War Book Review · Cited by 65
Self-citationNon-minimally coupled scalar fields and isolated horizons
Ashtekar, A., Corichi, A., & Sudarsky, D. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/15/310 · Cited by 64
Self-citationPerturbative Finiteness in Spin-Foam Quantum Gravity
Crane, L., Perez, A., & Rovelli, C. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.181301 · Cited by 64
Is Barbero's Hamiltonian formulation a Gauge Theory of Lorentzian Gravity?
Samuel, J. (2000) · CERN Document Server (European Organization for Nuclear Research) · Cited by 64
An algebraic extension of Dirac quantization: examples
Ashtekar, A., & Tate, R. S. (1994) · CERN Document Server (European Organization for Nuclear Research) · Cited by 63
Self-citationEssay: Initial Conditions for a Universe
Martin Bojowald, A. (2003) · General Relativity and Gravitation · doi:10.1023/a:1026257806654 · Cited by 60
The Interface of Knots and Physics
Kauffman, L. H. (1996) · Proceedings of symposia in applied mathematics · doi:10.1090/psapm/051 · Cited by 60
General Relativity and Gravitation
Lawrie, I. D. (2012) · CRC Press eBooks · doi:10.1201/b12906-9 · Cited by 60
Spectrum of the volume operator in quantum gravity
Loll, R. (1996) · Utrecht University Repository (Utrecht University) · Cited by 59
Diffeomorphism covariant representations of the holonomy-flux -algebra
Oko w, A., & Lewandowski, J. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/16/302 · Cited by 58
Self-citationNon-minimal couplings, quantum geometry and black-hole entropy
Ashtekar, A., & Corichi, A. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/20/310 · Cited by 57
Self-citationRecent Developments in Non-Perturbative Quantum GravityPreprint
Smolin, L. (1992) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9202022 · Cited by 57
Gravitons from a loop representation of linearized gravity
Varadarajan, M. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.66.024017 · Cited by 56
Black hole entropy calculations based on symmetries
Dreyer, O., Ghosh, A., & Wiśniewski, J. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/10/308 · Cited by 56
Gaul, M., & Rovelli, C. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/9/301 · Cited by 56
Yang-Mills analogues of the Immirzi ambiguity
Gambini, R., Obregón, O., & Pullin, J. A. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.59.047505 · Cited by 56
Spin Foam Quantization and AnomaliesPreprint
Martin Bojowald, A., & Pérez, A. (2003) · Cited by 56
Spin foam models of Riemannian quantum gravity
Baez, J. C., Christensen, J. D., Halford, T. R., & Tsang, D. C. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/18/301 · Cited by 54
Three dimensional loop quantum gravity: coupling to point particles
Noui, K., & Pérez, A. (2004) · CERN Document Server (European Organization for Nuclear Research) · Cited by 54
(3+1)-dimensional spin foam model of quantum gravity with spacelike and timelike components
Pérez, A., & Carlo Rovelli, C. (2001) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.64.064002 · Cited by 52
Refined Algebraic Quantization: Systems with a single constraintPreprint
Marolf, D. M. (1995) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9508015 · Cited by 52
Minisuperspaces: Observables and Quantization
Ashtekar, A., Tate, R. S., & Uggla, C. (1993) · CERN Document Server (European Organization for Nuclear Research) · Cited by 52
Self-citationOn the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theoriesPreprint
Sahlmann, H., & Thiemann, T. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0302090 · Cited by 51
Quantum horizons and black hole entropy: Inclusion of distortion and rotation
Ashtekar, A., Engle, J., & Broeck, C. V. D. (2004) · CERN Document Server (European Organization for Nuclear Research) · Cited by 51
Self-citationOn the relation between the connection and the loop representation of quantum gravity
Pietri, R. D. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1/009 · Cited by 50
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Cited by
Sorted by citations
Quantum nature of the big bang: Improved dynamics
Ashtekar, A., Pawlowski, T., & Singh, P. (2006) · Physical Review D · doi:10.1103/physrevd.74.084003 · Cited by 1,147
“Finally, as emphasized in section I, a key limitation of the present work is that the theory is not obtained through a systematic symmetry reduction of full LQG.”
BackgroundInfluentialSelf-citationQuantum Nature of the Big Bang
Ashtekar, A., Pawlowski, T., & Singh, P. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.141301 · Cited by 825
Self-citationMathematical structure of loop quantum cosmology
Ashtekar, A., Bojowald, M., & Lewandowski, J. (2003) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2003.v7.n2.a2 · Cited by 762
Self-citationBlack-hole entropy in loop quantum gravity
Meissner, K. A. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/22/015 · Cited by 720
The Spin-Foam Approach to Quantum Gravity
Perez, A. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-3 · Cited by 677
Metadata
- Authors
- Ashtekar, A., & Lewandowski, J.
- Affiliations
- Pennsylvania State University (US)
- Max Planck Society (DE)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2004-07-10
- Volume
- 21
- Issue
- 15
- Pages
- R53-R152
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2070707213
- Cited by
- 1,951
- References
- 268
- Citations by year
- 2026: 81 · 2025: 145 · 2024: 97 · 2023: 70 · 2022: 64 · 2021: 75 · 2020: 68 · 2019: 79 · 2018: 62 · 2017: 72 · 2016: 97 · 2015: 68 · 2014: 91 · 2013: 88 · 2012: 107
- FWCI
- 64.56
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- Max Planck Digital Library (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0090091)
- Alexander von Humboldt-Stiftung
- Pennsylvania State University
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy 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
- loop quantum gravity, background independence, quantum geometry, unification of quantum mechanics and general relativity, non-perturbative quantum gravity
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