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Geometric Quantization of String Theory Using Twistor Approach

  • A. D. Popov
  • A. G. Sergeev

Abstract

The geometric quantization scheme for the string theory is formulated in terms of a symplectic twistor bundle over the phase manifold.

Keywords

Line Bundle Geometric Quantization Projective Representation Holomorphic Line Bundle Siegel Disc 
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.

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References

  1. 1.
    M. J. Bowick, S. G. Rajeev, The holomorphic geometry of closed bosonic string theory and Diff(S1)/S1, Nucl. Phys. B293:348 (1987)MathSciNetADSCrossRefGoogle Scholar
  2. 1a.
    M. J. Bowick, S. G. Rajeev,Anomalies as curvature in complex geometry, Nucl. Phys. B296:1007 (1988).MathSciNetADSCrossRefGoogle Scholar
  3. 2.
    K. Pilch, N. P. Warner, Holomorphic structure of superstring vacua, Class. Quantum Grav. 4:1183 (1987)MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 2a.
    A. A. Kirillov, D. V. Juriev, Kähler geometry of the infinite-dimensional homogeneous space M = Diff(S1)/Rot(S1), Funkc. anal. i ego pril. 21:35, N 4 (1987) (in Russian)Google Scholar
  5. 2b.
    D. K. Hong, S. G. Rajeev, Universal Teichmüller space and Diff(S1)/S1, Commun. Math. Phys. 135:401 (1991)MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. 2c.
    S. Nag, A. Verjovsky, Diff(S1) and the Teichmüller spaces, Commun. Math. Phys. 130:123 (1990)MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 2d.
    A. Popov, A. Sergeev, Infinite dimensional Kähler manifolds and strings, Publ. IRMA (Lille) 28 (1992), N 2.Google Scholar
  8. 3.
    R. Penrose, Nonlinear gravitons and curved twistor theory, Gen. Relat. Grav. 7:31 (1976)MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. 3a.
    N. J. Hit chin, A. Karlhede, U. Lindstrøm, M. Roček, Hyperkähler metrics and supersymmetry, Commun. Math. Phys. 108:535 (1987)ADSzbMATHCrossRefGoogle Scholar
  10. 3b.
    S. Salamon, Quaternionic Kähler manifolds, Invent. math. 67:143 (1982).MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. 4.
    I. Vaisman, Symplectic twistor spaces, J. Geom. Phys. 3:507 (1986).MathSciNetADSzbMATHCrossRefGoogle Scholar
  12. 5.
    A. A. Kirillov, Geometric quantization, in:“Itogi nauki i tehn. Sovr. probl. matem. Fund. naprav., vol. 4”, VINITI, Moscow (1985) (in Russian)Google Scholar
  13. 5a.
    J. Sniatycki, “Geometric quantization and quantum mechanics”,Springer, New York (1980)zbMATHCrossRefGoogle Scholar
  14. 5b.
    N. J. M. Woodhouse, “Geometric quantization”,2nd ed., Clarendon Press, Oxford (1992).zbMATHGoogle Scholar
  15. 6.
    M. F. Atiyah, “Geometry of Yang-Mills Fields”,Scuola Norm. Super., Pisa (1979).zbMATHGoogle Scholar
  16. 7.
    A. Pressley, G. Segal, “Loop Groups”,Clarendon Press, Oxford (1986).zbMATHGoogle Scholar
  17. 8.
    G. Segal, Unitary representations of some infinite dimensional groups, Commun. Math. Phys. 80:301 (1981).ADSzbMATHCrossRefGoogle Scholar
  18. 9.
    Ju. A. Neretin, Representations of Virasoro and affine algebras, in: “Itogi nauki i tehn. Sovr. probl. matem. Fund. naprav., vol. 22”, VINITI, Moscow (1983) (in Russian).Google Scholar
  19. 10.
    R. Goodman, N. Wallach, Structure of unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle, Amer. J. Math. 347:69 (1984).MathSciNetzbMATHGoogle Scholar
  20. 11.
    B. L. Feigin, Semi-infinite cohomologies of Kac-Moody and Virasoro Lie algebras, Uspehi mat. nauk 39:195, N 2 (1984) (in Russian)MathSciNetzbMATHGoogle Scholar
  21. 11a.
    I. B. Frenkel, H. Garland, G. J. Zuckerman, Semi-infinite cohomology and string theory, Proc. Nat. Acad. Sci. USA 83:8442 (1986).MathSciNetADSzbMATHCrossRefGoogle Scholar
  22. 12.
    J. Mickelsson, String quantization on group manifolds and the holomorphic geometry of Diff(S1)/S1, Commun. Math. Phys. 112:653 (1987).MathSciNetADSzbMATHCrossRefGoogle Scholar
  23. 13.
    P. Goddard, D. Olive, Kac-Moody and Virasoro algebras in relation to quantum physics, Int. J. Mod. Phys. Al:303 (1986).MathSciNetADSGoogle Scholar
  24. 14.
    D. Gepner, E. Witten, String theory on group manifolds, Nucl. Phys. B278:493 (1986).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • A. D. Popov
    • 1
  • A. G. Sergeev
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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