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

导出并推广了三维费米子理论中与偶维轴反常有关的一个低能定理。将该定理推广到不具有平移不变性的系统。该定理也适用于有磁场的系统。在局域态区域的霍尔电导的精确量子化，而不考虑相互作用和无序的显示。磁场中的Ward-Takahashi恒等式使得霍尔电导是一个拓扑缠绕数，并满足精确的低能定理。材料效应和四维量子电动力学效应对量子化霍尔电导没有影响。

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.