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Quantum field theory with gravity and anomalies

具有引力和异常的量子场论

基本信息

批准号：
63540219
负责人：
FUJIKAWA Kazuo
金额：
$ 0.83万
依托单位：
HIROSHIMA UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1988
资助国家：
日本
起止时间：
1988 至 1989
项目状态：
已结题

项目摘要

The main subjects of this research project, namely, the problems related to anomalies, topology and Riemann surfaces received much attention recently.As for the specific results of the present research project, K. Fujikawa studied the detailed behavior of non-critical strings. By regarding the non- critical string theory as a 2-dimensional quantum gravity with anomalies, it was shown that the BRS symmetry is quite naturally defined for a free non- critical string. The string interactions are, however, rather involved due to the topological constraints related to the Riemann-Roch theorem (or ghost number anomaly).T. Kimura formulated a general quantum treatment of constrained systems, which are closely related to the quantum gravity. The applications of this formulation are left for the future.A. Hosoya studied the various problems related to the topology changes in quantum gravity. To be specific, he analyzed the vanishing mechanism of the cosmological constant due to baby universes in the path integral formalism. At the same time, he discovered a new instanton-like gravitational solution. As for 3-dimensional quantum gravity, he gave a nice canonical formulation by using the Teichmuller parameters as dynamical variables.S. Uehara continued the study of super-strings and super-particle. In particular, he succeeded in the general formulation to deal with the deformations of super-Riemann surfaces. This analysis, which is mathematically interesting, is hoped to provide a new insight into the dynamics of super- strings.

本研究课题的主要内容，即与反常、拓扑和黎曼曲面有关的问题，近年来受到了广泛的关注。Fujikawa研究了非临界弦的详细行为。把非临界弦理论看作是一个二维反常量子引力，证明了BRS对称性是自由非临界弦的自然定义。然而，由于与黎曼-罗克定理（或鬼数反常）有关的拓扑约束，弦相互作用是相当复杂的。木村提出了约束系统的一般量子处理方法，这与量子引力密切相关。这一公式的应用留待将来。细谷研究了与量子引力拓扑变化有关的各种问题。具体来说，他在路径积分形式主义中分析了婴儿宇宙导致宇宙常数消失的机制。与此同时，他发现了一个新的类瞬子引力解。对于三维量子引力，他用Teichmuller参数作为动力学变量，给出了一个很好的正则表达式。上原继续研究超弦和超粒子。特别是，他成功地在一般制定处理变形的超黎曼曲面。这种分析在数学上很有趣，希望能为超弦的动力学提供新的见解。