Combinatorial quantization of the Hamiltonian Chern-Simons theory I
Open accessThe 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.
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 field theory and the Jones polynomial
Witten, E. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01217730 · Cited by 4,758 · see citing works
Kassel, C. (1994) · Cited by 4,424 · see citing works
Current algebra and Wess-Zumino model in two dimensions
Knizhnik, V. G., & Zamolodchikov, A. B. (1984) · Nuclear Physics B · doi:10.1016/0550-3213(84)90374-2 · Cited by 1,838 · see citing works
Fusion rules and modular transformations in 2D conformal field theory
Verlinde, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90603-7 · Cited by 1,537 · see citing works
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
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 1,066 · see citing works
Remarks on the canonical quantization of the Chern-Simons-Witten theory
Elitzur, S., Moore, G., Schwimmer, A., & Seiberg, N. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90436-7 · Cited by 906 · see citing works
On quantum gauge theories in two dimensions
Witten, E. (1991) · Communications in Mathematical Physics · doi:10.1007/bf02100009 · Cited by 762 · see citing works
Chern-Simons perturbation theory. II
Axelrod, S., & Singer, I. M. (1994) · Journal of Differential Geometry · doi:10.4310/jdg/1214454681 · Cited by 362 · see citing works
Geometric quantization of Chern-Simons gauge theory
Axelrod, S., Della Pietra, S., & Witten, E. (1991) · Journal of Differential Geometry · doi:10.4310/jdg/1214446565 · Cited by 350 · see citing works
Central extensions of quantum current groups
Reshetikhin, N., & Semenov-Tian-Shansky, M. A. (1990) · Letters in Mathematical Physics · doi:10.1007/bf01045884 · Cited by 337 · see citing works
REPRESENTATIONS Of THE ALGEBRA U q ( sl (2)), q-ORTHOGONAL POLYNOMIALS AND INVARIANTS OF LINKS
Kirillov, A. N., & Reshetikhin, N. (1990) · Advanced series in mathematical physics · doi:10.1142/9789812798329_0012 · Cited by 309 · see citing works
Nest, R., & Tsygan, B. L. (1995) · Communications in Mathematical Physics · doi:10.1007/bf02099427 · Cited by 262 · see citing works
BRAID STATISTICS IN LOCAL QUANTUM THEORY
Fröhlich, J. M., & Gabbiani, F. (1990) · Reviews in Mathematical Physics · doi:10.1142/s0129055x90000107 · Cited by 236 · see citing works
Quasi Hopf quantum symmetry in quantum theory
Mack, G., & Schomerus, V. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90350-k · Cited by 180 · see citing works
Self-citationQuantization of symplectic orbits of compact Lie groups by means of the functional integral
Alekseev, A., Faddeev, L. D., & Shatashvili, S. L. (1988) · Journal of Geometry and Physics · doi:10.1016/0393-0440(88)90031-9 · Cited by 169 · see citing works
Self-citationDerivation of the Verlinde formula from Chern-Simons theory and the G/G model
Blau, M., & Thompson, G. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90538-z · Cited by 159 · see citing works
Relativistic Calogero-Moser model as gauged WZW theory
Gorsky, A., & Nekrasov, N. A. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(94)00499-5 · Cited by 152 · see citing works
Perturbative expansion of Chern-Simons theory with non-compact gauge group
Bar-Natan, D., & Witten, E. (1991) · Communications in Mathematical Physics · doi:10.1007/bf02101513 · Cited by 145 · see citing works
The Chern-Simons theory and knot polynomials
Fröhlich, J. M., & King, C. (1989) · Communications in Mathematical Physics · doi:10.1007/bf02124336 · Cited by 143 · see citing works
Quasi-Hopf Algebras and Knizhnik-Zamolodchikov Equations
Drinfeld, V. (1989) · Research reports in physics · doi:10.1007/978-3-642-84000-5_1 · Cited by 141 · see citing works
On the Wess-Zumino-Witten models on Riemann surfaces
Bernard, D. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90236-2 · Cited by 101 · see citing works
Two dimensional lattice gauge theory based on a quantum group
Buffenoir, E., & Roche, P. (1995) · Communications in Mathematical Physics · doi:10.1007/bf02099153 · Cited by 99 · see citing works
Quasi-quantum groups, knots, three-manifolds, and topological field theory
Altschuler, D., & Coste, A. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02096567 · Cited by 91 · see citing works
Hidden quantum groups inside Kac-Moody algebra
Alekseev, A., Faddeev, L. D., & Semenov-Tian-Shansky, M. A. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02097628 · Cited by 85 · see citing works
Self-citationRepresentation theory of Chern-Simons observables
Alekseev, A., & Schomerus, V. (1996) · Duke Mathematical Journal · doi:10.1215/s0012-7094-96-08519-1 · Cited by 83 · see citing works
Self-citationQuasi-quantum groups, knots, three-manifolds, and topological field theory
Altschüler, D., & Coste, A. (1992) · Project Euclid (Cornell University) · Cited by 83 · see citing works
A combinatorial approach to topological quantum field theories and invariants of graphs
Karowski, M., & Schrader, R. (1993) · Communications in Mathematical Physics · doi:10.1007/bf02096773 · Cited by 34 · see citing works
Combinatorial expression for universal Vassiliev link invariant
Piunikhin, S. (1995) · Communications in Mathematical Physics · doi:10.1007/bf02099581 · Cited by 33 · see citing works
Integrability in Hamiltonian Chern-Simons theoryPreprint
Alekseev, A. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9311074 · Cited by 24 · see citing works
Self-citationLocalization in GWZW and Verlinde formulaPreprint
Gerasimov, A. A. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9305090 · Cited by 23 · see citing works
q-deformed lattice gauge theory and 3-manifold invariants
BOULATOV, D. V. (1993) · Research at the University of Copenhagen (University of Copenhagen) · Cited by 23 · see citing works
Construction of Field Algebras with Quantum Symmetry from Local Observables
Schomerus, V. (1994) · Cited by 21 · see citing works
Self-citationq-DEFORMED LATTICE GAUGE THEORY AND 3-MANIFOLD INVARIANTS
BOULATOV, D. V. (1993) · International Journal of Modern Physics A · doi:10.1142/s0217751x93001259 · Cited by 18 · see citing works
Mack, G., & Schomerus, V. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02096941 · Cited by 16 · see citing works
Self-citationA construction of topological quantum field theories from 6J-symbols
Durhuus, B., Jakobsen, H. P., & Nest, R. (1992) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(05)80012-x · Cited by 14 · see citing works
Quantum Symmetry in Quantum Theory
Mack, G., & Schomerus, V. (1992) · NATO ASI series. Series B : Physics · doi:10.1007/978-1-4615-3472-3_12 · Cited by 13 · see citing works
Self-citationRepresentation Theory of Chern Simons ObservablesPreprint
Alekseev, A., & Schomerus, V. (1995) · arXiv (Cornell University) · doi:10.48550/arxiv.q-alg/9503016 · Cited by 13 · see citing works
Self-citationThe antipode of and star operations in a Hopf algebra
Scheunert, M. (1993) · Journal of Mathematical Physics · doi:10.1063/1.530384 · Cited by 11 · see citing works
Construction of field algebras with quantum symmetry from local observables
Schomerus, V. (1995) · Communications in Mathematical Physics · doi:10.1007/bf02101601 · Cited by 11 · see citing works
Self-citationSU(2) WZNW Model at Higher Genera from Gauge Field Functional IntegralPreprint
Gawędzki, K. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9312051 · Cited by 5 · see citing works
A quantum group version of quantum gauge theories in two dimensionsPreprint
Karowski, M., Schrader, R. (. U. B. (. I. F. T. P., & Quantenphysik, T. U. B. (. S. 2. D. U. (1992) · Cited by 3 · see citing works
Quasi quantum group covariant q-oscillators
Schomerus, V. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90310-l · Cited by 1 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 4
- [3][3] A. Sudbury, Non-commuting coordinates and differential operators in: Quantum groups, T. Curtright et al. (eds), World Scientific, Singapore 1991 -
- [6][6] V.V. Fock, A.A. Rosly, Poisson structures on moduli of flat connections on Riemann surfaces and r-matrices , preprint ITEP 72-92, June 1992, Moscow -
- [10][10] V.G. Drinfel'd, Quantum groups , Proc. ICM (1987) 798 -
- [23][23] P. Cartier, Construction Combinatoire des Invariants de Vassiliev-Kontsevich des Nœds , preprint of the Erwin Schr¨ odinger Institute ESI 15 (1993), Vienna, Austria. -
Cited by
Sorted by citations
Three-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
Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
Alexandrov, S., & Livine, E. R. (2003) · Physical Review D · doi:10.1103/physrevd.67.044009 · Cited by 141 · see citing works
Perez, A., & Pranzetti, D. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/14/145009 · Cited by 53 · see citing works
- Authors
- Alekseev, A. Y., Grosse, H., & Schomerus, V.
- Affiliations
- Uppsala University (SE)
- University of Vienna (AT)
- Harvard University (US)
- Venue
- Communications in Mathematical Physics
- Published
- 1995-09
- Volume
- 172
- Issue
- 2
- Pages
- 317-358
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W1998354025
- Cited by
- 176
- References
- 44
- Citations by year
- 2026: 4 · 2025: 7 · 2024: 11 · 2023: 2 · 2022: 8 · 2021: 12 · 2020: 10 · 2019: 10 · 2018: 6 · 2017: 11 · 2016: 2 · 2015: 9 · 2014: 7 · 2013: 5 · 2012: 3
- FWCI
- 12.01
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Communications in Mathematical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Keywords
- Chern-Simons theory, Hamiltonian quantization, algebra of observables
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
