Applications of Gauge Theories to Condensed-Matter Physics

规范理论在凝聚态物理中的应用

基本信息

批准号：
03640273
负责人：
SHIZUYA Kenichi
金额：
$ 0.83万
依托单位：
KYOTO UNIVERSITY (1992)Osaka University (1991)
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1992
项目状态：
已结题

项目摘要

Symmetries play an important role in physics. In particular, quantum collective phenomena such as superconductivity and superfluidity are intimately tied to the symmetry of the underlying microscopic dynamics, and the framework of gauge theories is particularly suited for the description of such collective phenomena. In view of this, under the Grant-in-Aid over the past two-year period, we have studied(1)the quantum Hall effect in condensed-matter physics from the viewpoint of gauge theories and(2)phenomena reflecting the geometric nature of gauge fields (gauge anomalies, the Aharonov- Bohm effect, etc.).1. We have presented a field-theoretic description of the quantum Hall system and shown that the quantized Hall conductance is a kind of adiabatic invariant unaffected by disorder; this explains the exceptional precision in Hall quantization. Subsequently we have studied the edge-current dynamics and found that a picture of the Hall current flowing along the edges of a sample is obtained as a consequence of localization and gauge invariance.2. There has recently been considerable interest in induced Chern-Simons terms in 1+2 dimensions in connection with the quantum Hall effect. It is shown that the Chern-Simons terms are induced as a response of the Dirac sea to applied electromagnetic fields; a paper is now in preparation.3. A paper pointing out that the Aharonov-Bohm and Aharonov-Casher effects are tied to electromagnetic angular momentum was presented.4. We have examined the consistency and current algebras of anomalous gauge theories in four dimensions and confirmed the connection between the anomaly and the Schwinger term.

对称性在物理学中起着重要作用。特别是，量子集体现象（例如超导性和超流量）与基本微观动力学的对称性密切相关，并且规格理论的框架特别适合描述这种集体现象。考虑到这一点，在过去两年的赠款中，我们从量规理论的角度研究了（1）凝结物理学中的量子霍尔效应，以及（2）反映了规格场（规范异常，Aharonov-Bohm-Bohm-Bohm效应等）的现象。我们已经介绍了量子厅系统的现场理论描述，并表明量化的霍尔电导是一种绝热不受障碍影响的绝热。这解释了大厅量化中的出色精度。随后，我们研究了边缘电流动力学，发现沿着样品边缘流动的霍尔电流的图像是由于定位和规格不变性而获得的。2。最近，与量子霍尔效应有关的1+2维度的诱发的Chern-Simons项有很大的兴趣。结果表明，Chern-Simons项是作为狄拉克海对应用电磁场的响应而诱导的。现在正在准备一篇论文3。提出的一篇论文指出，Aharonov-Bohm和Aharonov-Casher效应与电磁角动量有关。4。我们已经检查了四个维度的异常仪表理论的一致性和当前代数，并确认了异常和舒林格项之间的联系。