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.

该研究项目的主要主题，即，与异常，拓扑和Riemann表面有关的问题最近受到了很多关注。由于本研究项目的具体结果，K。Fujikawa研究了非临界串的详细行为。通过将非临界弦理论作为具有异常的二维量子重力，这表明BRS对称性是自然而然地定义的，用于自由的非临界字符串。但是，由于与Riemann-Roch定理（或幽灵数异常）相关的拓扑约束，弦相互作用涉及。木村制定了对约束系统的一般量子处理，该处理与量子重力密切相关。此配方的应用留给未来。 Hosoya研究了与量子重力的拓扑变化有关的各种问题。具体来说，他分析了由于路径整体形式主义中的婴儿宇宙而导致的宇宙学常数的消失机制。同时，他发现了一种新的类似Instanton的重力解决方案。至于三维量子重力，他通过将TeichMuller参数用作动力学变量来提供了一个不错的规范公式。 Uehara继续研究超级弦和超级粒子。特别是，他成功地完成了一般配方，以应对超级帝国表面的变形。这项在数学上有趣的分析希望为超级字符串的动态提供新的见解。