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Twistor quantization of the space of half-differentiable vector functions on the circle revisited

  • Armen Sergeev
Article

Abstract

We discuss the twistor quantization problem for the classical system (V d ,A d ), represented by the phase space V d , identified with the Sobolev space H 0 1/2 (S 1,ℝ d ) of half-differentiable vector functions on the circle, and the algebra of observables A d , identified with the semi-direct product of the Heisenberg algebra of V d and the algebra Vect(S 1) of tangent vector fields on the circle.

Keywords

twistor quantization Sobolev space of half-differentiable functions group of diffeomorphisms of the circle 

MSC(2000)

58E20 53C28 32L25 

References

  1. 1.
    Bowick M J, Rajeev S G. The holomorphic geometry of closed bosonic string theory and Diff S 1/S 1. Nucl Phys, B293: 348–384 (1987)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Davidov J, Sergeev A G. Twistor quantization of loop spaces. Proc Steklov Inst Math, 217: 1–90 (1997)MathSciNetGoogle Scholar
  3. 3.
    Sergeev A G. Kähler Geometry of Loop Spaces (in Russian). Moscow: Moscow Centre for Continuous Math Education, 2001Google Scholar
  4. 4.
    Kobayashi S, Nomizu K. Foundations of Differential Geometry. New York-London: Interscience Publishers, 1963MATHGoogle Scholar
  5. 5.
    Segal G. Unitary representations of some infinite dimensional groups. Comm Math Phys, 80: 301–342 (1981)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Goodman R, Wallach N R. Projective unitary positive-energy representations of Diff(S 1). J Funct Anal, 63: 299–321 (1985)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Bowick M J, Lahiri A. The Ricci curvature of Diff S 1/SL(2, ℝ). J Math Phys, 29: 1979–1981 (1988)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Shale D. Linear symmetries of free boson field. Trans Amer Math Soc, 103: 149–167 (1962)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Pressley A, Segal G. Loop Groups. Oxford: Clarendon Press, 1986MATHGoogle Scholar

Copyright information

© Science in China Press and Springer Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Mathematical PhysicsSteklov Mathematical InstituteMoscowRussia

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