Advertisement

The chern-simons theory and quantized moduli spaces of flat connections

  • Anton Yu. Alekseev
  • Volker Schomerus
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 469)

Keywords

Modulus Space Conjugacy Class Hopf Algebra Poisson Bracket Marked Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V.V. Fock, A.A. Rosly, Poisson structures on moduli of flat connections on Reimann surfaces and r-matrices, preprint ITEP 72-92, June 1992, MoscowGoogle Scholar
  2. 2.
    A. Yu. Alekseev, H. Grosse, V. Schomerus, Combinatorial quantization of the Hamiltonian Chern Simons theory I, HUTMP 94-B336, HEP-TH/9403066, Commun. Math. Phys., to appearGoogle Scholar
  3. 3.
    A. Yu. Alekseev, H. Grosse, V. Schomerus, Combinatorial quantization of the Hamiltonian Chern Simons theory II, HUTMP 94-B336, HEP-TH/9408097, Commun. Math. Phys., to appear.Google Scholar
  4. 4.
    A.Yu. Alekseev, V. Schomerus, Representation Theory of Chern-Simons Observables, Q-ALG/9503016.Google Scholar
  5. 5.
    A.Yu. Alekseev, Integrability in the Hamiltonian Chern-Simons theory, Uppsala preprint HEP-TH/9311074, St-Petersburg Math. J., vol. 6, no. 2 (1994) 53Google Scholar
  6. 6.
    D. V. Boulatov, q-deformed lattice gauge theory and three manifold invariants, Int. J. Mod. Phys. A8, (1993), 3139CrossRefADSMathSciNetzbMATHGoogle Scholar
  7. 7.
    A.Yu. Alekseev, L.D. Faddeev, M.A. Semenov-Tian-Shansky Hidden Quantum groups inside Kac-Moody algebras, Commun. Math. Phys. 149, no. 2 (1992) p.335.CrossRefADSMathSciNetzbMATHGoogle Scholar
  8. 8.
    E. Buffenoir, Ph. Roche, Two dimensional lattice gauge theory based on a quantum group, preprint CPTH A 302-05/94 and HEP-TH/9405126Google Scholar
  9. 9.
    J. Andersen, J. Mattis, N. Reshetikhin, to be publishedGoogle Scholar
  10. 10.
    S.A. Frolov, Hamiltonian lattice gauge models and the Heisenberg double, Munich preprint LMU-TPW 95-3, HEP-TH/9502121.Google Scholar
  11. 11.
    M. Atiyah, R. Bott, The Yang-Mills equation over Riemann surfaces, Phil. Trans. of the Royal Soc. of London, ser A 308 (1982) 523ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    S. Elitzur, G. Moore, A. Schwimmer, N. Seiberg, Remarks on the canonical quantization of the Chern-Simons-Witten theory, Nucl. Phys. 326, (1989) 108CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    W. Goldman, Invariant functions on Lie groups and Hamiltonian flows of surface group representations, Invent. Math. 85 (1986) 263; W. Goldman, The symplectic nature of fundamental groups of surfaces, Adv. Math. 54 (1984) 200CrossRefADSMathSciNetzbMATHGoogle Scholar
  14. 14.
    N. Reshetikhin, V. G. Turaev, Ribbon graphs and their invariants derived from quantum groups, Commun. Math. Phys. 127, (1990) 1CrossRefADSMathSciNetzbMATHGoogle Scholar
  15. 15.
    G. Mack, V. Schomerus, Quasi Hopf quantum symmetry in quantum theory, Nucl. Phys. B370 (1992) 185CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    A. Sudbury, Non-commuting coordinates and differential operators in: Quantum groups, T. Curtright et al. (eds), World Scientific, Singapore 1991Google Scholar
  17. 17.
    L.D. Faddeev, N.Yu. Reshetikhin, L.A. Takhtadzhyan, Quantization of Lie Groups and Lie Algebras, Algebra and Analysis 1 (1989), 1 and Leningrad Math. J. Vol. 1 (1990), No. 1Google Scholar
  18. 18.
    DeConcini, V. Kac, Representations of quantum groups at roots of 1, in Progress in Mathematics vol. 92, Birkhäuser 1990Google Scholar
  19. 19.
    G. Lusztig, Finite dimensional Hopf algebras arising from quantized universal enveloping algebras, J. Am. Math. Soc. vol. 3 1 (1990) 257CrossRefMathSciNetzbMATHGoogle Scholar
  20. 20.
    J. Fröhlich, F. Gabbiani, Braid statistics in local quantum theory, Rev. Math. Phys. 2 (1991) 251CrossRefGoogle Scholar
  21. 21.
    N. Reshetikhin, V. G. Turaev, Invariants of 3-manifolds via link polynomials and quantum groups, Invent. Math. 103 (1991) 547CrossRefADSMathSciNetzbMATHGoogle Scholar
  22. 22.
    E. Verlinde, Fusion rules and modular transformations in 2D conformal field theory, Nucl. Phys. B 300 (1988) 360CrossRefADSMathSciNetzbMATHGoogle Scholar
  23. 23.
    E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121, (1989) 351CrossRefADSMathSciNetzbMATHGoogle Scholar
  24. 24.
    S. Axelrod, S. Della Pietra, E. Witten, Geometric quantization of Chern-Simons gauge theory, J. Diff. Geom. 33 (1991) 787zbMATHGoogle Scholar
  25. 25.
    V. Knizhnik, A. B. Zamolodchikov, Current algebra and Wess-Zumino model in two dimensions, Nucl. Phys. B247 (1984) 83CrossRefADSMathSciNetzbMATHGoogle Scholar
  26. 26.
    V.G. Drinfel'd, Quasi Hopf algebras and Knizhnik Zamolodchikov equations, in: Problems of modern quantum field theory, Proceedings Alushta 1989, Research reports in physics, Springer Verlag Heidelberg 1989Google Scholar
  27. 27.
    D. Kazhdan, G. Lusztig, Tensor structures arising from affine Lie algebras I/II, J. Am. Math. Soc. vol. 6 4 (1993) 905CrossRefMathSciNetzbMATHGoogle Scholar
  28. 28.
    M. Finkelberg, Fusion Categories, Harvard University thesis, May 1993Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Anton Yu. Alekseev
    • 1
  • Volker Schomerus
    • 2
  1. 1.Institut für Theoretische PhysikETH-HönggerbergZürichSwitzerland
  2. 2.II. Institut für Theoretische PhysikUniversität HamburgHamburgGermany

Personalised recommendations