Spin Networks in Gauge Theory
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The first attempt [12] was largely exploratory, considered only the simplest loop states and eigenvalues, and made no claim of completeness.
“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]
Section 4, Theorem 1 (page unavailable), states that spin network states on embedded graphs span the full kinematical Hilbert space, rather than considering only the simplest loop states without a completeness claim. The paper does leave the construction of all diffeomorphism-invariant physical states open (Section 5), but that is a different qualification. The passages found do not report the claimed eigenvalue calculations. (LLM, conf=0.82)
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measuredIn the present language, the first attempt [12] corresponds to restricting to bi-valent graphs.
“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]
Section 4, “Spin Network States” (page unavailable), defines Baez’s spin network states on any embedded graph, not only bi-valent graphs. Section 5, “Conclusions” (page unavailable), describes a single-loop graph as a particular example; it does not make bi-valent graphs a restriction of the paper’s approach. (LLM, conf=0.79)
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measuredThe 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, leads to continuum geometries.
“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]
The Introduction (page unavailable) describes quantum-gravity spin-network states using graphs with labeled edges, supporting the claim’s graph-based aspect. Neither that passage nor the Conclusions (page unavailable) says that densely packed excitations yield continuum geometry when coarse-grained above the Planck scale. (LLM, conf=0.82)
Experimental — accuracy not yet measuredFor bi-valent graphs, apart from an overall numerical factor, the present results reduce to those of [12].
“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]
Area operators were first examined in the loop representation.
“Area operators were first examined in the loop representation.”
From Quantum theory of geometry: I. Area operators (1997) · cites this paper as [12]
Section 3, “The Loop Representation,” describes the representation and its mathematical framework, but does not discuss area operators. Searches for “area operators first examined” and “area operator area surface geometric operators” found no passage addressing when or where area operators were first examined. The indexed passages provide no page numbers. (LLM, conf=0.72)
Experimental — accuracy not yet measured
The distributional character of geometry at the microscopic level is present even in semi-classical states that approximate classical geometries macroscopically.
“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]
The Introduction and Conclusions describe spin-network states and generalized measures, but do not address whether microscopic geometry remains distributional in semiclassical states. Searches for semiclassical states approximating classical geometry and for distributional microscopic geometry found no passage making that connection; no page numbers were available in our copy. (LLM, conf=0.72)
Experimental — accuracy not yet measuredThis class includes all Euclidean simplicial four dimensional gravity models except that of Iwasaki.
“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]
Spin network states whose graph is the 1-skeleton of the dual complex define states in L2(A_S/G_S), and these states span that space.
“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]
Spin networks form a convenient basis of kinematical states.
“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]
Spin networks have largely replaced collections of loops as the basic picture of quantum 3-geometries.
“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]
The value of a vertex is determined by the matrix elements of the hamiltonian constraint, which are known.
“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]
Matrix elements of the hamiltonian constraint operator have been computed explicitly in [34], using the methods developed in [23].
“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]
The vertex A_v(σ) of general relativity is given by a product of Wigner 3n-j symbols.
“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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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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
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 · see citing works
Temperley-Lieb recoupling theory and invariants of 3-manifolds
Kauffman, L. H., & LINS, S. L. S. (1994) · Cited by 377 · see citing works
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 · see citing works
(1994) · doi:10.1093/oso/9780198534907.003.0002 · Cited by 165 · see citing works
Representation Theory of Analytic Holonomy C* Algebras
Ashtekar, A., & Lewandowski, J. (1993) · arXiv · doi:10.48550/arxiv.gr-qc/9311010 · Cited by 155 · see citing works
Generalized measures in gauge theory
Baez, J. C. (1994) · Letters in Mathematical Physics · doi:10.1007/bf00761713 · Cited by 139 · see citing works
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 · see citing works
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 104 · see citing works
Baez, J. C. (1993) · arXiv · doi:10.48550/arxiv.hep-th/9305045 · Cited by 78 · see citing works
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 · see citing works
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 · see citing works
Knots and Quantum Gravity: Progress and ProspectsPreprint
Baez, J. C. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9410018 · Cited by 27 · see citing works
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 · see citing works
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 · see citing works
Recent Mathematical Developments in Quantum General RelativityPreprint
Ashtekar, A. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9411055 · Cited by 13 · see citing works
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 · see citing works
Flagged first, then by citations
1 of the 21 references couldn’t be matched to a known paper.
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
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Ashtekar, A., & Singh, P. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/21/213001 · Cited by 1,205 · see citing works
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Ashtekar, A., Baez, J., Corichi, A., & Krasnov, K. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.904 · Cited by 1,105 · see citing works
Self-citation(1998) · doi:10.12942/lrr-1998-1 · Cited by 917 · see citing works
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Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/4/011 · Cited by 750 · see citing works
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Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/4/012 · Cited by 247 · see citing works
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Oriti, D. (2001) · Reports on Progress in Physics · doi:10.1088/0034-4885/64/12/203 · Cited by 201 · see citing works
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Carlip, S. J., Chiou, D.-W., Ni, W.-T., & Woodard, R. (2015) · International Journal of Modern Physics D · doi:10.1142/s0218271815300281 · Cited by 66 · see citing works
Loop quantum gravity and quanta of space: a primerPreprint
Carlo Rovelli, C., & Upadhya, P. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9806079 · Cited by 66 · see citing works
Quasi-local holographic dualities in non-perturbative 3D quantum gravity
Dittrich, B., Goeller, C., Livine, E. R., & Riello, A. (2018) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aac606 · Cited by 46 · see citing works
Major, S. (1999) · American Journal of Physics · doi:10.1119/1.19175 · Cited by 44 · see citing works
A Prehistory of n-Categorical Physics
Baez, J. C., & Lauda, A. D. (2011) · Cambridge University Press eBooks · doi:10.1017/cbo9780511976971.003 · Cited by 46 · see citing works
Self-citationChiou, D.-W. (2014) · International Journal of Modern Physics D · doi:10.1142/s0218271815300050 · Cited by 41 · see citing works
New Constraints for Canonical General RelativityPreprint
Reisenberger, M. (1995) · Cited by 38 · see citing works
SU( N ) Quantum Yang–Mills theory in two dimensions: A complete solution
Ashtekar, A., Lewandowski, J., Marolf, D., Mourão, J., & Thiemann, T. (1997) · Journal of Mathematical Physics · doi:10.1063/1.532146 · Cited by 35 · see citing works
Simple model for quantum general relativity from loop quantum gravity
Carlo Rovelli, C. (2011) · Journal of Physics Conference Series · doi:10.1088/1742-6596/314/1/012006 · Cited by 46 · see citing works
Microscopic Description of 2D Topological Phases, Duality, and 3D State SumsPreprint
Kádár, Z., Marzuoli, A., & Rasetti, M. (2013) · Cited by 34 · see citing works
Quantization of Diffeomorphism-Invariant Theories with FermionsPreprint
Baez, J. C., & Krasnov, K. V. (1998) · Cited by 37 · see citing works
Self-citationThe classical limit and the form of the hamiltonian constraint in nonperturbative quantum gravity
Smolin, L. (1996) · arXiv · doi:10.48550/arxiv.gr-qc/9609034 · Cited by 33 · see citing works
Quantum Geometry and Gravity: Recent AdvancesPreprint
Ashtekar, A. (2001) · Cited by 36 · see citing works
A combinatorial approach to diffeomorphism invariant quantum gauge theories
Zapata, J. A. (1997) · Journal of Mathematical Physics · doi:10.1063/1.532159 · Cited by 32 · see citing works
A new Hamiltonian for the topological BF phase with spinor networks
Bonzom, V., & Livine, E. R. (2012) · Journal of Mathematical Physics · doi:10.1063/1.4731771 · Cited by 35 · see citing works
Loop Quantum Gravity à la Aharonov–Bohm
Eugenio Bianchi, A. (2014) · General Relativity and Gravitation · doi:10.1007/s10714-014-1668-4 · Cited by 34 · see citing works
- 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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