場の理論における低エネルギー定理とその応用についての研究

低能定理及其在场论中的应用研究

• 批准号: 61540189
• 负责人: ISHIKAWA Kenzo
• 金额: $ 0.7万
• 依托单位: HOKKAIDO 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: 1986
• 资助国家: 日本
• 起止时间: 1986 至 1988
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61540189/
• 关键词: low energy theorem; axial anomaly; quantum Hall effect; tensor-glveball; Ward-Takahashi identity; topological invariant; QED; 局在; 量子電気力学(QED); くり込み理論; 軸性アノマリー; Chern-Simon項; エネルギー運動量テンソル; グルーボール; θ(1720); トポロジー; 量子電気力学

A low energy theorem in three dimensional fermion theory, which is connected with even dimensional axial anomaly, is derived and extended. An extension of the theorem to systems without translational invariance is made. The theorem is also applied to the system with magnetic field. The exact quantization of the Hall conductance in the localized state region regardless of interactions and disorders in shown. Ward-Takahashi identity in the magnetic field leads that the Hall conductance is a topological winding number and satisfies the exact low energy theorm. The material effect and four dimensional quantum electrodynamics effect do not modify the quantized Hall conductance.

推导并推广了三维费米子理论中与偶维轴向异常相关的低能定理。将该定理推广到没有平移不变性的系统。该定理也适用于有磁场的系统。显示了局部状态区域中霍尔电导的精确量化，无论相互作用和紊乱如何。磁场中的 Ward-Takahashi 恒等式表明霍尔电导是拓扑绕数并且满足精确的低能定理。材料效应和四维量子电动力学效应不会改变量子化霍尔电导。

项目成果

K. Ishikawa: "Magnetic Field Induced Multi-component QED_3 and Quantum Hall Effect" Zeit fur Physik. C33. 41-45 (1986)

K. Ishikawa：“磁场感应多分量 QED_3 和量子霍尔效应”Zeit Fur Physik。

K.Ishikawa: Zeitschrift f【¨!u】r Physik C. 33. 41-45 (1986)

K. Ishikawa：Zeitschrift f【¡!u】r Physik C. 33. 41-45 (1986)

K.Ishikawa: Nuclear Physics. B280〔FS18〕. 523-548 (1987)

K.Ishikawa：核物理。B280〔FS18〕523-548（1987）。

K.Ishikawa.: Nuclear Physics. B280. 523-548 (1987)

K.Ishikawa.：核物理学。

N.Imai et al: Nuclear Physics B.

N.Imai 等人：核物理学 B.