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.

藤川继续研究二维重力的量子机械方面，并试图阐明量子异常在量子重力中的作用。具体来说，他试图一方面基于动力学三角剖分，并根据liouville的行动来理解离散的重力之间的直接关系。特别是，他试图理解Weyl异常的表现以及在动态三角测量中相关的Liouville作用。在此过程中，他获得了韦尔对称性破裂及其在动力学三角剖分方案中的重新构成的相当清晰的物理图，以及坐标的概念。他还提出了QCD.Fujikawa中单环β函数的简单非图形计算，还继续对与量规理论中的Baryon违规有关的量子隧道进行了过去的研究。他调查了如何克服激体分裂的缺点，尽管大部分受试者都供将来进行研究。Kubo在扩展相位的基础上给出了量子异常和相关异常换向因子的一般制定。该方法可以应用于多种受试者。他在二维重力和黑洞蒸发的独立配方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。”