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

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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 1/20 (S 1,ℝd) 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.

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References

  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)

    Article  MathSciNet  Google Scholar 

  2. Davidov J, Sergeev A G. Twistor quantization of loop spaces. Proc Steklov Inst Math, 217: 1–90 (1997)

    MathSciNet  Google Scholar 

  3. Sergeev A G. Kähler Geometry of Loop Spaces (in Russian). Moscow: Moscow Centre for Continuous Math Education, 2001

    Google Scholar 

  4. Kobayashi S, Nomizu K. Foundations of Differential Geometry. New York-London: Interscience Publishers, 1963

    MATH  Google Scholar 

  5. Segal G. Unitary representations of some infinite dimensional groups. Comm Math Phys, 80: 301–342 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  6. Goodman R, Wallach N R. Projective unitary positive-energy representations of Diff(S 1). J Funct Anal, 63: 299–321 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bowick M J, Lahiri A. The Ricci curvature of Diff S 1/SL(2, ℝ). J Math Phys, 29: 1979–1981 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  8. Shale D. Linear symmetries of free boson field. Trans Amer Math Soc, 103: 149–167 (1962)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pressley A, Segal G. Loop Groups. Oxford: Clarendon Press, 1986

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Physics, Steklov Mathematical Institute, Moscow, 119991, Russia

    Armen Sergeev

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  1. Armen Sergeev
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Correspondence to Armen Sergeev.

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Dedicated to Professor Zhong TongDe on the occasion of his 80th birthday

This work was supported by the RFBR (Grant Nos. 06-02-04012, 08-01-00014), the program of Support of Scientific Schools (Grant No. NSH-3224.2008.1), and Scientific Program of RAS “Nonlinear Dynamics”

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Sergeev, A. Twistor quantization of the space of half-differentiable vector functions on the circle revisited. Sci. China Ser. A-Math. 52, 2714–2729 (2009). https://doi.org/10.1007/s11425-009-0201-9

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  • DOI: https://doi.org/10.1007/s11425-009-0201-9

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