Quantum symmetry in field theory and its applications

场论中的量子对称性及其应用

• 批准号: 04640285
• 负责人: FUJIKAWA Kazuo
• 金额: $ 0.96万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1992
• 资助国家: 日本
• 起止时间: 1992 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-04640285/
• 关键词: Field theory; Anomaly; Quantum Gravity; Tunneling effect; Topology; アノマリー(量子異常)

Fujikawa continued his research of quantum mechanical aspects of two-dimensional 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 two-dimensional 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 one-loop 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.

藤川继续他对二维引力的量子力学方面的研究，并试图阐明量子异常在量子引力中的作用。具体来说，一方面，他试图理解基于动力三角测量的离散重力与基于刘维尔作用的更常规的二维重力之间的直接关系。特别是，他试图理解外尔异常的表现以及动态三角测量中相关的刘维尔作用。在此过程中，他获得了相当清晰的外尔对称性破缺及其在动态三角测量方案中的恢复的物理图像以及坐标的概念。他还提出了 QCD 中单环 beta 函数的简单非图解计算。藤川还继续了过去与规范理论中的重子数破坏相关的量子隧道效应的研究。他研究了如何克服瞬子微积分的缺点，尽管大部分课题都留待将来研究。久保在扩展相空间的基础上给出了量子异常和相关反常换向子的一般公式。这种方法可以应用于多种学科；他在二维引力和黑洞蒸发的规范独立公式中获得了非常有趣的结果。

项目成果

T.Fujiwara et al.: "A new insight into BRST anomalies in string theory." Nuclear Physics B391. 211-228 (1993)

T.Fujiwara 等人：“对弦理论中 BRST 异常的新见解。”

K.Fujikawa,M.Ninomiya: "Semi-classical continuum limit of dynamical triangulation and Weyl symmetry" Nuclear Physics. B. (1993)

K.Fujikawa，M.Ninomiya：“动态三角测量和韦尔对称性的半经典连续极限”核物理。

K.Fujikawa: "A semi-classical continuum limit of dynamical triangulation and Weyl symmetry" Nuclear Physics B. 391. 675-694 (1993)

K.Fujikawa：“动态三角测量和韦尔对称性的半经典连续极限”核物理 B. 391. 675-694 (1993)

T.Fujiwara,Y.Igarashi J.Kubo,K.Maeda: "A new insight into BRST anomalies in string theory" Nuclear Physics. B. (1993)

T.Fujiwara、Y.Igarashi J.Kubo、K.Maeda：“弦理论中 BRST 异常的新见解”核物理。

K.Fujikawa: "BRST symmetry in string and membrane theories." Progress of Theoretical Physics Suppl.114. 185-199 (1993)

K.Fujikawa：“弦和膜理论中的 BRST 对称性。”