Anomalies in Gauge Theories and Related Phenomena

对称性在物理学中扮演着重要的角色。然而，经典对称性有时会在量子化后失效，它们的量子修改被称为反常。因此，反常现象代表了量子本质的一些深层结构，并经常成为理解量子本质的物理现象的关键。有鉴于此，在过去两年的资助下，我们(1)追求反常规范理论的一致量子化，以阐明反常的作用，(2)从规范场理论的角度研究凝聚态物理中的量子输运现象。我们考察了二维和四维反常规范理论的一致性和流代数。这项工作是与东北大学的S.Miyake博士合作完成的。(1)电荷密度波(Cdw)：我们研究了一维导体中电荷密度波输运现象的对称性特征，从其基本的手征对称性和chi…出发。更多的左向异常。特别指出，在一维电子-声子系统的长波结构中出现了基于Kac-Moody代数的局域手征对称性，而CDW与这种局域对称性有关的无质量模被识别出来。这项工作是与纽约城市学院(CCNY)的B.Sakita教授合作完成的。(2)任意子：最近人们对服从分数统计的准粒子(任意子)与高温超导有关的问题非常感兴趣。我们在三维规范理论的框架内研究了任意子，结果表明，当任意子彼此接近时，大范围分离的任意子实现的分数统计消失。(3)量子霍尔效应：我们构造了一个集合场理论，它用(1+1)维的多分量狄拉克场来描述磁场中的电子，并研究了霍尔电导与Berry位相的量子化。一篇论文现在正在准备中。较少

Symmetries play an important role in physics. Classical symmetries, however, sometimes fail to survive quantization ; and their quantum modifications are called anomalies. Anomalies thus represent some deep structures of quantum nature and often serve as a key in understanding physical phenomena of traly quantum nature. In view of this, under the Grant-in-Aid over the past two-year period, we have (1) pursued consistent quantization of anomalous gauge theories to clarify the roles of anomalies, and (2) have investigated quantum transport phenomena in condensed-matter physics from the viewpointof gauge-field theories.1. We have examined the consistency and current algebras of anomalous gauge theories two and four dimensions. This work was done in collaboration with Dr. S. Miyake at Tohoku University.2. (1) Charge-density waves (CDW) : We have studied symmetry-related features of the CDW transport phenomenon in one-dimensional conductors in terms of its underlying chiral symmetry and chi … More ral anomaly. In particular, it is Pointed out that a local chiral symmetry based on the Kac-Moody algebra arises in the long-wavelength structure of one-dimensional electron-phonon systems ; and the CDW are identified with massless modes associated with this local symmetry. This work was done in collaboration with Prof. B. Sakita at the City College of New York (CCNY).(2) Anyons : There has recently been considerable interest in quasi-particles obeying fractional statistics (anyons) in connection with high-temperature superconductivity. We have studied anyons within the framework of 3-dimensional gauge theories and shown that fractional statistics realized for widely-separated anyons disappears when anyons come close to each other.(3) Quantum Hall Effect : We have constructed a collective-field theory which describes electrons in a magnetic field in terms of a multi-component Dirac field in (1+1) dimensions, and studied quantization of the Hall conductance in relation to Berry's phase. A paper is now in preparation. Less