Gravity based on Generalized Canonical Formalism

本研究项目的目的是在Batalin-Fradikin-Vilkoviski发展的广义哈密顿形式的基础上，研究具有局域规范不变性的系统（如引力理论和弦理论）的量子化。在过去的两年里，我们进行了二维超引力理论作为反常规范理论的量子化。在那里，异常取消super-Liouville字段被成功地引入到识别原来的第二类约束系统与规范固定版本的第一类系统。这些结果已在9月18-22日在京都大学数学科学研究所举行的“20周年国际BRS对称性研讨会”上报告。1995.我们的方法也被应用到具有反对称张量场的拓扑BF理论中，我们用基于广义上同调分析的方法研究了该系统是否包含规范反常BFV形式主义。1995年9月在日本中央大学举行的日本物理学会秋季会议上报告了该系统没有BRS异常的主要结果。

The purpose of this reserach project is to study quantization of systems with local gauge invarinace such as gravitational theories and string theories on the basis of the generalized hamiltonian formalism developed by Batalin-Fradikin-Vilkoviski. In the last two years for term of the project, we have been carried out quantization of two-dimensional super-gravity theory as an anomalous gauge theory. There, the anomaly-cancelling super-Liouville fields are succesfully introduced to identify the original second-class constrained system with a gauge-fixed version of a first-class system. These results have been reported at "The International Symposium on BRS symmetry on the Occasion of Its 20th Anniversary" which was held at the Research Institute for Matimatical Sciences, Kyoto University for Septmber 18-22,1995.Our method has been applied also to a topological BF theory with an antisymmetric tensor field.We investigated if the system can contain gauge anomaly by using the general cohomological analysis based on the BFV formalism. The main results that the system have no BRS anonalies was reported at The Autumn Meeting of the Japan Physical Sociaty held at Chuoh University, September 1995.