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
“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
“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]
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
“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]
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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Citations
Cites
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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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