Quantum symmetry in field theory and its applications
Project/Area Number  04640285 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
核・宇宙線・素粒子

Research Institution  The University of Tokyo 
Principal Investigator 
FUJIKAWA Kazuo The University of Tokyo Graduate School of Science, Professor, 大学院・理学系研究科, 教授 (30013436)

CoInvestigator(Kenkyūbuntansha) 
KUBO Jisuke College of General Education Kanazawa University, Associate Professor, 教養部, 助教授 (40211213)

Project Fiscal Year 
1992 – 1993

Project Status 
Completed(Fiscal Year 1993)

Budget Amount *help 
¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 1993 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1992 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Field theory / Anomaly / Quantum Gravity / Tunneling effect / Topology / 場の理論 / 量子異常(アノマリー) / 量子重力 / トンネル効果 / トポロジー / アノマリー(量子異常) 
Research Abstract 
Fujikawa continued his research of quantum mechanical aspects of twodimensional gravity and tried to clarify the role of quantum anomaly in quantum gravity. To be specific, he tried to understand the direct relation between the discretized gravity on the basis of dynamical triangulation, on the one hand, and the more conventional twodimensional gravity on the basis of Liouville action. In particular, he tried to understand the manifestation of the Weyl anomaly and the associated Liouville action in the dynamical triangulation. In the process, he obtained a rather clear physcal picture of the Weyl symmetry breaking and its retoration in the dynamical triangulation scheme together with the notion of coordinates. He also presented a simple nondiagramatic calculation of oneloop beta function in QCD. Fujikawa also continued the past study of quantum tunneling in connection with the baryon number violation in the gauge theory. He investigated how to overcome the shortcoming of the instanton calculus although much of the subject is left for future investigation. Kubo gave a general formulation of quantum anomaly and related anomalous commutators on the basis of the extended phase space. This method can be applied to a wide variety of subjects ; he obtained quite interesting results in gauge independent formulation of two dimensional gravity and the evaporation of black holes.

Report
(4results)
Research Output
(24results)