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.

本研究项目的主要课题，即与异常、拓扑和黎曼曲面相关的问题近年来备受关注。至于本研究项目的具体成果，K. Fujikawa研究了非临界弦的详细行为。通过将非临界弦理论视为具有异常的二维量子引力，结果表明，对于自由非临界弦，BRS 对称性是很自然地定义的。然而，由于与黎曼-罗赫定理（或鬼数异常）相关的拓扑约束，弦相互作用相当复杂。木村提出了与量子引力密切相关的约束系统的通用量子处理。该配方的应用留待未来。细谷研究了与量子引力拓扑变化相关的各种问题。具体来说，他在路径积分形式主义中分析了由于婴儿宇宙而导致宇宙常数消失的机制。与此同时，他发现了一种新的类瞬子引力解。至于3维量子引力，他通过使用Teichmuller参数作为动力学变量给出了一个很好的规范公式。上原继续进行超弦和超粒子的研究。特别是，他成功地提出了处理超黎曼曲面变形的通用公式。这项分析在数学上很有趣，有望为超弦动力学提供新的见解。