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Chinese Physics C> 1989, Vol. 13> Issue(6) : 503-511 

ON GEOMETRIC QUANTIZATION FOR BOSONIC STRING (Ⅱ)

  •  Institute of High Energy Physics,Academia Sinica P.O.Box 918,Beijing2 Institute of Theoretical Physics,Academia Sinica,P.O.Box 2735,Beijing

  • The Hilbert space and the representation of the generators of Virasoro algebra for bosonic string under a holomorphic polarization are given in this paper,It is shown that the contre term of Virasoro algebra may be interpreted as curvature of a holomorphic vector bundle (holomorphic Fock bundle) on coset space G11=G/H where G denotes the conformal transformation group and H the one-parameter subgroup generated by the generator L0.The condition of the conformal anomaly cancellation may be expressed as the vanishing curvature of the bundle which is obtained by the product of the holomorphic Fock bundle and the holomorphic ghost vacuum bundle.The geometric interpretations of both classical and quantized BRST operators,ghost and antighost operators are also discussed.
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    [1] 虞跃，郭汉英，关于玻色弦的几何量子化(一)，将在《高能物理与核物理》发表.[2] M. Rolrick and S. G. Rajeev, Phys. Rev. Lett., 58(1987), 353; Nucl. Phys., B293(1987), 34.8.J. Mickelsson, Commun. Math. Phys., 112(1987), 653.D. Harri, D. K. Hong, P. Rarnond and V. G. Rodgers, Nucl. Phys., B294(1987), 556.Z. Y. Zhao, K. Wu and T. Saito, Phys. Lett., E199(1987), 37.[3] K. Pilch and N. P. Warner, Class. Quant. Grav., 4(1987), 1183.[4] C. Chevalley, The Algebric Theory of Spinors (Columbia Univ. Press (1954)).[5] H. Y. Guo and K. Wu, in Proceedings of the Paris-Meudon Colloquium, 1986, ed. by H. J. de Vega and N. Scnchez, World Sci. 1987.[6] L. B. Frenkel, H. Garland and G. J. Zucherman, Proc. Nat'l Acad. Sci., (U. S. A.) 83(1986), 8442.

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YU Yue and GUO Han-Ying. ON GEOMETRIC QUANTIZATION FOR BOSONIC STRING (Ⅱ)[J]. Chinese Physics C, 1989, 13(6): 503-511.
YU Yue and GUO Han-Ying. ON GEOMETRIC QUANTIZATION FOR BOSONIC STRING (Ⅱ)[J]. Chinese Physics C, 1989, 13(6): 503-511. shu
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Received: 1900-01-01
Revised: 1900-01-01
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ON GEOMETRIC QUANTIZATION FOR BOSONIC STRING (Ⅱ)

    Corresponding author: YU Yue,
  • Institute of High Energy Physics,Academia Sinica P.O.Box 918,Beijing2 Institute of Theoretical Physics,Academia Sinica,P.O.Box 2735,Beijing
  • Received Date: 1900-01-01
  • Accepted Date: 1900-01-01
  • Available Online: 1989-06-05

Abstract: The Hilbert space and the representation of the generators of Virasoro algebra for bosonic string under a holomorphic polarization are given in this paper,It is shown that the contre term of Virasoro algebra may be interpreted as curvature of a holomorphic vector bundle (holomorphic Fock bundle) on coset space G11=G/H where G denotes the conformal transformation group and H the one-parameter subgroup generated by the generator L0.The condition of the conformal anomaly cancellation may be expressed as the vanishing curvature of the bundle which is obtained by the product of the holomorphic Fock bundle and the holomorphic ghost vacuum bundle.The geometric interpretations of both classical and quantized BRST operators,ghost and antighost operators are also discussed.

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