The DOI matches its Crossref record; 20 of the 21 references it cites were found in a registry or an index.
Spin Networks in Gauge Theory
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“The first attempt [12] was largely exploratory. Thus, although the key ideas were recognized, the very simplest of loop states were considered and the simplest eigenvalues were looked at; there was no claim of completeness.”
From Quantum theory of geometry: I. Area operators (1997) · cites this paper as [12]
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“In the present language, this corresponds to restricting oneself to bi-valent graphs.”
From Quantum theory of geometry: I. Area operators (1997) · cites this paper as [12]
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In the citing paper
“Just as a polymer, although intrinsically 1-dimensional, exhibits 3-dimensional properties in sufficiently complex and densely packed configurations, the fundamental 1-dimensional excitations of geometry can be packed appropriately to provide a geometry which, when coarse-grained on scales much larger than the Planck length, lead us to continuum geometries [12,22].”
From Quantum theory of geometry: I. Area operators (1997) · cites this paper as [12]
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In the citing paper
“In this case, apart from an overall numerical factor (which does, however, have some conceptual significance) our results reduce to that of [12].”
From Quantum theory of geometry: I. Area operators (1997) · cites this paper as [12]
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In the citing paper
“Area operators were first examined in the loop representation.”
From Quantum theory of geometry: I. Area operators (1997) · cites this paper as [12]
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In the citing paper
“This is the case even in semi-classical states which approximate classical geometries macroscopically [12,22].”
From Quantum theory of geometry: I. Area operators (1997) · cites this paper as [12]
Experimental — accuracy not yet measuredIn the citing paper
“This class includes all Euclidean simplicial four dimensional gravity models except that of Iwasaki [28].”
From Spacetime as a Feynman diagram: the connection formulation (2001) · cites this paper as [28]
In the citing paper
“Then by a now familiar argument [13], defines a state in L 2 (A S /G S ), which we also call .Moreover, such spin network states span L 2 (A S /G S ).”
From Spin foam models (1998) · cites this paper as [13]
In the citing paper
“Indeed, since spin networks form a very convenient basis of kinematical states [13], they have largely replaced collections of loops as our basic picture of 'quantum 3-geometries'.”
From Spin foam models (1998) · cites this paper as [13]
In the citing paper
“Indeed, since spin networks form a very convenient basis of kinematical states [13], they have largely replaced collections of loops as our basic picture of 'quantum 3-geometries'.”
From Spin foam models (1998) · cites this paper as [13]
In the citing paper
“Their value is determined by the matrix elements of the hamiltonian constraint, which are known.”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [34]
In the citing paper
“Matrix elements of this operator have been computed explicitly in [34], using the methods developed in [23].”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [34]
In the citing paper
“The vertex A v ( σ ) of general relativity is given by a product of Wigner 3 n -j symbols [34].”
From “Sum over surfaces” form of loop quantum gravity (1997) · cites this paper as [34]
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Citations
Cites
Invariants of 3-manifolds via link polynomials and quantum groups
Reshetikhin, N., & Turaev, V. G. (1991) · Inventiones Mathematicae · doi:10.1007/bf01239527 · Cited by 1,492
Discreteness of area and volume in quantum gravity
Rovelli, C., & Smolin, L. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00150-q · Cited by 1,365
State sum invariants of 3-manifolds and quantum 6j-symbols
Turaev, V. G., & Viro, O. Y. (1992) · Topology · doi:10.1016/0040-9383(92)90015-a · Cited by 1,145
Ribbon graphs and their invaraints derived from quantum groups
Reshetikhin, N., & Turaev, V. G. (1990) · Communications in Mathematical Physics · doi:10.1007/bf02096491 · Cited by 1,017
Projective techniques and functional integration for gauge theories
Ashtekar, A., & Lewandowski, J. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531037 · Cited by 388
Temperley-Lieb recoupling theory and invariants of 3-manifolds
Kauffman, L. H., & LINS, S. L. S. (1994) · Cited by 387
Representations of the holonomy algebras of gravity and nonAbelian gauge theories
Ashtekar, A., & Isham, C. J. (1992) · Classical and Quantum Gravity · doi:10.1088/0264-9381/9/6/004 · Cited by 310
(1994) · doi:10.1093/oso/9780198534907.003.0002 · Cited by 165
Representation Theory of Analytic Holonomy C* Algebras
Ashtekar, A., & Lewandowski, J. (1993) · arXiv · doi:10.48550/arxiv.gr-qc/9311010 · Cited by 155
Generalized measures in gauge theory
Baez, J. C. (1994) · Letters in Mathematical Physics · doi:10.1007/bf00761713 · Cited by 139
Self-citationState sum invariants of 4-manifolds
Crane, L., Kauffman, L. H., & Yetter, D. N. (1997) · Journal of Knot Theory and Its Ramifications · doi:10.1142/s0218216597000145 · Cited by 139
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
Baez, J. C. (1993) · arXiv · doi:10.48550/arxiv.hep-th/9305045 · Cited by 78
Self-citationOn the constraints of quantum gravity in the loop representation
Brügmann, B., & Pullin, J. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90462-x · Cited by 40
TOPOLOGICAL MEASURE AND GRAPH-DIFFERENTIAL GEOMETRY ON THE QUOTIENT SPACE OF CONNECTIONS
LEWANDOWSKI, J. (1994) · International Journal of Modern Physics D · doi:10.1142/s0218271894000307 · Cited by 36
Knots and Quantum Gravity: Progress and ProspectsPreprint
Baez, J. C. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9410018 · Cited by 29
Self-citationMathematical Problems of Non-perturbative Quantum General RelativityPreprint
Ashtekar, A. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9302024 · Cited by 16
State-Sum Invariants of 4-Manifolds IPreprint
Crane, L., Kauffman, L. H., & Yetter, D. N. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9409167 · Cited by 16
Recent Mathematical Developments in Quantum General RelativityPreprint
Ashtekar, A. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9411055 · Cited by 13
Coherent State Transforms for Spaces of ConnectionsPreprint
Ashtekar, A., Lewandowski, J., Marolf, D. M., et al. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9412014 · Cited by 3
Research works printed but not linked: 2
- [14]14. R. Penrose, Angular momentum; an approach to combinatorial space time, in ``Quantum Theory and Beyond'' (T. Bastin, Ed.), Cambridge Univ. Press, Cambridge, UK, 1971.
- [16]16. C. Rovelli and L. Smolin, Loop representation for quantum general relativity, Nucl. Phys. B 331 (1990), 80 152.
Cited by
Sorted by citations
Background independent quantum gravity: a status report
Ashtekar, A., & Lewandowski, J. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/15/r01 · Cited by 1,951
Loop quantum cosmology: a status report
Ashtekar, A., & Singh, P. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/21/213001 · Cited by 1,205
Quantum geometry and black hole entropy
Ashtekar, A., Baez, J., Corichi, A., & Krasnov, K. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.904 · Cited by 1,105
Self-citation(1998) · doi:10.12942/lrr-1998-1 · Cited by 917
Quantum theory of geometry: I. Area operators
Ashtekar, A., & Lewandowski, J. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1a/006 · Cited by 852
Metadata
- Authors
- Baez, J. C.
- Affiliations
- University of California, Riverside (US)
- Corresponding author
- Baez, John C.
- ORCID
- Baez, John C.
- Venue
- Advances in Mathematics
- Publisher
- Elsevier BV
- Published
- 1996-02
- Volume
- 117
- Issue
- 2
- Pages
- 253-272
- ISSN
- 0001-8708 (ISSN-L)
- OpenAlex
- W1811947045
- Cited by
- 266
- References
- 21
- Citations by year
- 2026: 4 · 2025: 6 · 2024: 10 · 2023: 10 · 2022: 2 · 2021: 3 · 2020: 4 · 2019: 4 · 2018: 16 · 2017: 4 · 2016: 6 · 2015: 16 · 2014: 9 · 2013: 7 · 2012: 5
- FWCI
- 19.08
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Advances in Mathematics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Keywords
- spin networks, gauge theory, principal bundles, spin network states, orthonormal bases, unitary irreducible representations, intertwining operators, loop representation, quantum gravity, category theory
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