1992 Fiscal Year Final Research Report Summary
Applications of Gauge Theories to Condensed-Matter Physics
| Project/Area Number |
03640273
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
核・宇宙線・素粒子
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| Research Institution | KYOTO UNIVERSITY (1992)
Osaka University (1991) |
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Principal Investigator |
SHIZUYA Kenichi Yukawa Inst. for Theor. Phys.,Kyoto University,Professor, 基礎物理学研究所, 教授 (50154216)
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| Project Period (FY) |
1991 – 1992
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| Keywords | Gauge theories / Symmetry / Anomalies / Quantum Hall effect / Edge current / Aharonov-Bohm effect / Aharonov-Casher effect |
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| Research Abstract |
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.
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