Isomonodromic quantization of dimensionally reduced gravity

被引:26
作者
Korotkin, D
Nicolai, H
机构
[1] II Institute for Theoretical Physics, Hamburg University, Hamburg 22761
[2] Steklov Mathematical Institute, 191011 St. Petersburg
关键词
quantum gravity; integrable systems; isomonodromic quantization; dimensional reduction;
D O I
10.1016/0550-3213(96)00320-3
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
We present a detailed account of the isomonodromic quantization of dimensionally reduced Einstein gravity with two commuting Killing vectors. This theory constitutes an integrable ''midi-superspace'' version of quantum gravity with infinitely many interacting physical degrees of freedom. The canonical treatment is based on the complete separation of variables in the isomonodromic sectors of the model. The Wheeler-DeWitt and diffeomorphism constraints are thereby reduced to the Knizhnik-Zamolodchikov equations for SL(2,R). The physical states are manifestly invariant under the full diffeomorphism group. An infinite set of independent observables a la Dirac exists both at the classical and the quantum level. Using the discrete unitary representations of SL(2,R), we construct explicit quantum states. However, the problem of satisfying the additional constraints associated with the coset space SL(2,R)/SO(2) remains open. We briefly discuss the possible implications of our results for string theory.
引用
收藏
页码:397 / 439
页数:43
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