关于玻色弦的几何量子化(二)  

ON GEOMETRIC QUANTIZATION FOR BOSONIC STRING(Ⅱ)

作　　者：虞跃 郭汉英[2] 

机构地区：[1]中国科学院高能物理研究所 [2]中国科学院理论物理研究所

出　　处：《高能物理与核物理》1989年第6期503-511,共9页High Energy Physics and Nuclear Physics

摘　　要：本文给出在金纯极化下玻色弦的Hilbert空间和Virasoro代数生成元的表示.我们证明了Virasoro代数的中心项可以解释为弦的全纯Fock丛的曲率.反常相消条件是弦的全纯Fock丛和全纯鬼真空丛的乘积丛的曲率为零.我们还讨论了经典的和量子的BRST算子、鬼算子和反鬼算子的几何意义.The geometric quantization for bosonic strings is discussed in this paper. Relations among different polarizations and representations of operators in different polarizations are given. It is pointed out that the prequantization Hilbert space is the unitary representation of the conformal group where the centre term of Virasoro algebra does not exist but this representation is reducible. By polarization it is reduced into two projective representations with the phase factors with opposite signs. Then the conformal anomaly is obtained. In the viewpoint of geometric quantization, the emergence of the conformal anomaly stems from the fact that polarization is introduced because the quantum states of string must satisfy the uncertainty relation but all generators of conformal transformation don't preserve the same polarization.

关 键 词：玻色弦 几何量子化 算子 

分 类 号：O572.2[理学—粒子物理与原子核物理]