Journal of Differential Geometry

Geometric quantization of Chern-Simons gauge theory

Scott Axelrod, Steve Della Pietra, and Edward Witten

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

J. Differential Geom. Volume 33, Number 3 (1991), 787-902.

First available in Project Euclid: 26 June 2008

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58F06
Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 32G13: Analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15] 58D27: Moduli problems for differential geometric structures 81S10: Geometry and quantization, symplectic methods [See also 53D50] 81T40: Two-dimensional field theories, conformal field theories, etc.


Axelrod, Scott; Della Pietra, Steve; Witten, Edward. Geometric quantization of Chern-Simons gauge theory. J. Differential Geom. 33 (1991), no. 3, 787--902.

Export citation


  • [15] P. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, New York, 1978.
  • [16] V. Guillemin and S. Steinberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982) 515-538.
  • [17] J. Harer, The second homology group of the mapping class group of an orientable surface, Invent. Math. 72 (1982) 221-239.
  • [18] N. Hitchin, Flat connections and geometric quantization, Oxford preprint, 1989.
  • [19] N. Hitchin, Stable bundles and integrable systems, Duke Math. J. 54 (1987) 91-114.
  • [20] V. F. R. Jones, Hecke algebra representations of braid groups and link polynomials, Ann. of Math. (2) 126 (1987) 335-388.
  • [21] V. G. Knizhnik and A. B. Zamolodchikov, Current algebra and Wess-Zumino model in two dimensions, Nuclear Phys. B 247 (1984) 83.
  • [22] B. Kostant, Orbits, symplectic structures, and representation theory, Proc. U.S.-Japan Seminar in Differential Geometry (Kyoto, 1965), Quantization And Unitary Representations, Lecture Notes in Math., Vol. 170, Springer, Berlin, 1970, 87; Line Bun- dles And the Prequantized Schrodinger Equation, Coll. Group Theoretical Methods in Physics, Marseille, 1972, 81.
  • [23] G. Moore and N. Seiberg, Polynomial equations for rational conformal field theories, Phys. Lett. B 212 (1988) 360; Naturality in conformal field theory, Institute for Advanced Study, preprint HEP/88/31 (to appear in Nuclear Phys. B); Classical and quantum conformal field theory, Institute for Advanced Study, preprint HEP/88/39 (to appear in Nuclear Phys. B).
  • [24] D. Mumford and J. Fogarty, Geometric invariant theory, Springer, Berlin, 1982.
  • [25] M. S. Narasimhan and S. Ramanan, Deformations of the moduli space of vector bundles over an algebraic curve, Ann. of Math. (2) 101 (1975) 391-417.
  • [26] A. Pressley and G. Segal, Loop groups, Oxford Univ. Press, Oxford, 1988.
  • [27] D. Quillen, Determinants of Cauchy-Riemann operators over a Riemann surface, Functional Anal. Appl. 19 (1985) 31-34.
  • [28] T. R. Ramadas, I. M. Singer and J. Weitsman, Some comments on Chern-Simons gauge theory, MIT, preprint.
  • [29] D. Ray and I. Singer, R-Torsion and the Laplacian o nRiemannian manifolds, Advances in Math. 7 (1971) 145-210; Analytic torsion of complex manifolds, Ann. of Math. (2) 98 (1973) 154-177.
  • [30] N. Yu. Reshetikhin and V. G. Turaev, Invariants of three-manifolds via link polynomials and quantum groups, Math. Sci. Res. Inst. preprint, 1989.
  • [31] B. Schroer, Operator approach to conformal invariant quantum field theories and related problems, Nuclear Phys. 295 (1988) 586-616; K.-H. Rehren and B. Schroer, Einstein causality andArtin braids, FU preprint, 1987.
  • [32] A. Schwarz, The partition function of degenerate quadratic functional and Ray-Singer invariants, Lett. Math. Phys. 2 (1978) 247-252.
  • [33] A. S. Schwarz, New topological invariants arising in the theory of quantized fields, Abstract, Baku International Topological Conference, 1987.
  • [34] G. Segal, Two-dimensional conformal field theories and modular functors, IXth Internat. Conf. on Math. Physics (Swansea, July, 1988) (B. Simon, A. Truman, and I. M. Davies, eds.), Adam Hilger, 1989, 22-37.
  • [35] C. Simpson, Higgs bundles and local systems, moduli of representations of the fundamental group of a smooth projective variety, preprints.
  • [36] J. Sniatycki, Geometric quantization and quantum mechanics, Springer, New York, 1980.
  • [37] J.-M. Souriau, Quantification geometrique, Comm. Math. Phys. 1 (1966) 374;Structures des systemes dynamiques, Dunod, Paris, 1970.
  • [38] A. Tsuchiya and Y. Kanie, Conformal field theory and solvable lattice models, Advanced Studies Pure Math. 16 (1988) 297; Lett. Math. Phys. 13 (1987) 303-312.
  • [39] A. Tsuchiya, K. Ueno and Y. Yamada, Conformal field theory on universal family of stable curves with gauge symmetries, Max Planck Institute, preprint, 1989.
  • [40] E. Verlinde, Fusion rules and modular transformationsin 2d conformal field theory, Nuclear Phys. B 300 (1988) 360-376.
  • [41] E. Witten, Topological quantum field theory, Comm. Math. Phys. 117 (1988) 353-386.
  • [42] E. Witten, Quantum field theory and the Jones polynomial, Comm. Math. Phys. 121 (1989) 351-399.
  • [43] N. Woodhouse, Geometric quantization, Oxford Univ. Press, Oxford, 1980.