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Anomalies in Gauge Theories and Related Phenomena

规范理论的反常现象及相关现象

基本信息

批准号：
01540249
负责人：
SHIZUYA Ken-ichi
金额：
$ 1.54万
依托单位：
Osaka 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：
1989
资助国家：
日本
起止时间：
1989 至 1990
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01540249/
关键词：
Anomalies Chiral symmetry Gauge theories Charge density waves Anyons Kac-Moody algebra Quantum Hall effect High-T superconductivity 端数粒子統計

项目摘要

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

对称性在物理学中起着重要的作用。然而，经典对称性有时无法在量子化中幸存下来;它们的量子修改被称为异常。因此，反常代表了量子性质的某些深层结构，常常是理解真正量子性质的物理现象的一把钥匙。有鉴于此，在过去两年的补助金资助下，我们（1）对反常规范理论进行了一致的量子化，以澄清反常的作用，（2）从规范场理论的观点研究了凝聚态物理中的量子输运现象。我们研究了二维和四维反常规范理论的相容性和流代数.这项工作是与S博士合作完成的。东北大学的三宅。2. (1)电荷密度波（CDW）：我们研究了一维导体中CDW输运现象的手征对称性和气 ...更多信息拉尔异常。特别指出，一维电子-声子系统的长波结构中存在基于Kac-Moody代数的局部手征对称性，CDW与这种局部对称性相关的无质量模相对应.这项工作是与B教授合作完成的。纽约城市学院（CCNY）的Sakita。(2)任何人：最近有相当大的兴趣，准粒子服从分数统计（任意子）与高温超导性。我们已经在三维规范理论的框架内研究了任意子，并证明了当任意子彼此靠近时，对于广泛分离的任意子实现的分数统计消失。(3)量子霍尔效应：我们建立了一个集体场理论，它描述了在磁场中的电子在（1+1）维的多分量狄拉克场的条款，并研究了量子化的霍尔电导与Berry的相位。目前正在编写一份文件。少