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Cited by 57Algebraic structures and combinatorial modelsBlack Holes and Theoretical PhysicsNoncommutative and Quantum Gravity Theories

Topological field theory and the quantum double of SU(2)

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Bais, F.A., Muller, N.M.·1998·Nuclear Physics B
DOI 10.1016/s0550-3213(98)00572-0
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Crossref · 10.1016/s0550-3213(98)00572-0

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  • The quantum group structure of these brackets can be expressed in terms of the quantum double of the Lorentz group.

    “several authors have further explored the quantum group structure of these brackets, which can be expressed in terms of the quantum double of the Lorentz group [37, 36, 61, 201].”

    From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [36]

    Section 9 (pp. 39, 42) identifies D(SO(2,1)), the quantum double of the 2+1-dimensional Lorentz group, as the symmetry governing the quantum theory of 2+1 gravity. The cited paper does not establish that the specific brackets in the citing sentence have that structure; its detailed treatment of the quantum double concerns SU(2). (LLM, conf=0.82)

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Cites

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Research works printed but not linked: 23

  1. [1][1] Birmingham, D., and M. Blau, M. Rakowski, G. Thompson, Topological field theory , Phys. Reports, Vol. 209 (1991), Nrs. 4&5. -
  2. [3][3] Verlinde, E.P., and H.L. Verlinde, Conformal field theory and geometric quantization , in Superstrings '89 , Proceedings of the Trieste Spring School, World Scientific (1990), 422-449. -
  3. [4][4] Gomez, C., and M. Ruiz-Altaba, and G. Sierra, Quantum Groups in Two-dimensional Physics , Cambridge University Press, 1996. -
  4. [6][6] Dijkgraaf, R, and V. Pasquier, P. Roche, Quasi Hopf algebras, group cohomology and orbifold models , Nucl. Phys. B (Proc. Suppl.) 18B (1990), 60-72. -
  5. [8][8] Wild Propitius, M.D.F. de, and F.A. Bais, Discrete gauge theories , in Particles and Fields , editor G.W. Semenoff, CRM Series in Math. Phys., Springer Verlag (to be published), and M.D.F. de Wild Propitius, Topological Interactions in Broken Gauge Theories , PhD thesis University of Amsterdam, 1995. -
  6. [9][9] Dijkgraaf, R., and E. Witten, Topological gauge theories and group cohomology , Comm. Math. Phys. 129 (1990), 393. -
  7. [10][10] Koornwinder, T.H., and N.M. Muller, The quantum double of a (locally) compact group , Journal of Lie Theory, Vol.7 (1997) Nr.1, 33-52. Erratum in Vol.8 (1998) Nr.1. -
  8. [11][11] Koornwinder T.H., and F.A. Bais, N.M. Muller, Tensor product representations of the quantum double of a compact group , q-alg/9712042 (to be published in Comm. Math. Phys.) - · arXiv
  9. [14][14] Kirillov, A.A., Elements of the Theory of Representations , Springer-Verlag, 1976. -
  10. [15][15] Rawnsley, J.H., Representations of a semi-direct product by quantization , Math. Proc. Camb. Phil. Soc. 78 (1975), 345-350. -
  11. [16][16] Landsman, N.P., Mathematical Topics between Classical and Quantum Mechanics , Springer Mathematical Monographs, 1998,to appear. -
  12. [17][17] Woodhouse, N., Geometric Quantization , Clarendon Press, Oxford, 1980. -
  13. [19][19] Faddeev, L., and R. Jackiw, Hamiltonian reduction of unconstrained and constrained systems , Phys. Rev. Letters, Vol.60 (1988), 1692-1694. -
  14. [20][20] Marsden, J.E., and T. Ratiu, A. Weinstein, Semidirect products and reduction in mechanics , Trans. Amer. Math. Soc., Vol. 281 No.1, (1984), 147-177. -
  15. [22][22] Rno, J.S., Clebsch-Gordan coefficients and special functions related to the Eulcidean group in three-space , Journal of Math. Physics, Vol. 15 , No.12 (1974), 2042-2047. -
  16. [23][23] Aharonov, Y, and D. Bohm, Significance of electromagnetic potentials in the quantum theory , Phys. Rev. Vol.115, No.3., 485-491. -
  17. [24][24] Varshalovich, D.A., and A.N. Moskalev, V.K. Khersonski, Quantum Theory of Angular Momentum , World Scientific, 1988. -
  18. [26][26] Verlinde, E.P., A note on braid statistics and the nonabelian Aharonov-Bohm effect , Proceeding of the Int. Colloquium on Modern Quantum Field Theory, Bombay, World Scientific, 1990. -
  19. [28][28] Helgasson, S., Groups and Geometric Analysis , Academic Press, Inc., 1984. -
  20. [32][32] Drinfel'd, V.G., Quantum groups , in Proceedings of the I.C.M., Berkeley, (1986), American Math. Soc., 1987, 798-820. -
  21. [33][33] Chari, V., and A. Pressley, A Guide to Quantum Groups , Cambridge University Press, 1994. -
  22. [34][34] Majid, S., Foundations of Quantum Group Theory , Cambridge University Press, 1995. -
  23. [35][35] Tjin T., Introduction to quantized Lie groups and algebras , Int. Journal of Mod. Physics A, Vol. 7 No. 25 (1992), 6175-6213.

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Authors
Bais, F. A., & Muller, N. M.
Affiliations
Institute for Theoretical Physics Amsterdam (NL)
Corresponding author
  • Bais, F.A.
  • Muller, N.M.
Venue
Nuclear Physics B
Publisher
Elsevier BV
Published
1998-10
Volume
530
Issue
1-2
Pages
349-400
ISSN
0550-3213 (ISSN-L)
DOI
10.1016/s0550-3213(98)00572-0
OpenAlex
W2100748192
Cited by
57
References
1
Citations by year
2026: 1 · 2023: 1 · 2022: 2 · 2021: 1 · 2019: 2 · 2018: 4 · 2017: 2 · 2016: 1 · 2015: 2 · 2014: 8 · 2013: 2
FWCI
1.62
Type
journal article
Language
en
Open access
Licence
Locations
  • Nuclear Physics B (publishedVersion)
  • UvA-DARE (University of Amsterdam) (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • UvA-DARE (University of Amsterdam) (submittedVersion)
  • Data Archiving and Networked Services (DANS) (submittedVersion)
  • arXiv (Cornell University)
Funders
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Topics
  • Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
Keywords
topological field theory, quantum double, SU(2), 2+1 dimensions, fusion rules, R-matrix, unitary irreducible representations, differential cross section, quantum gravity

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