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1992 Fiscal Year Final Research Report Summary

Applications of Gauge Theories to Condensed-Matter Physics

Research Project

Project/Area Number 03640273
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 核・宇宙線・素粒子
Research InstitutionKYOTO UNIVERSITY (1992)
Osaka University (1991)

Principal Investigator

SHIZUYA Kenichi  Yukawa Inst. for Theor. Phys.,Kyoto University,Professor, 基礎物理学研究所, 教授 (50154216)

Project Period (FY) 1991 – 1992
KeywordsGauge theories / Symmetry / Anomalies / Quantum Hall effect / Edge current / Aharonov-Bohm effect / Aharonov-Casher effect
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.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] S.MIYAKE: "Consistency and current algebras of a Non-Abelan chiral gauge theory in four dimensions" Physical Review. D45. 2090-2097 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.SHIZUYA: "Gauge invatiance,adiabatic change and quantized Hall conductance" Physical Review. B45. 11143-11150 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] J.Macda: "The aharonov-Bohm and Aharonov-Casher effects and electromagnetic angular momentum" (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.SHIZUYA: "Gauge invariance and cdge-currcnt dynamics in the quantum Hall effect" (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N.FUMITA: "Induced Chern-Simons term and intrinsic polarezation of the Dirac sea" (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 静谷 謙一: "量子異常(物理学最前線シリーズ第29巻に収録)" 共立出版株式会社, 54 (1992)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S. Miyake: "Consistency and current algebras of a non-Abelian chiral gauge theory in four dimensions." Physical Review. D45. 2090-2097 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Shizuya: "Gauge invariance, adiabatic change, and quantized Hall conductance." Physical Review. B45. 11143-11150 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J. Maeda,: "The Aharonov-Bohm and Aharonov-Casher effects and electromagnetic angular momentum." (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Shizuya: "Gauge Invariance and edge-current dynamics in the quantum Hall effect." (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Fumita: "Induced Chern-Simons term and intrinsic polarization of the Dirac sea." (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Shizuya: Kyoritsu Shuppan. Anomalies (in Butsurigaku Saizensen Series vol. 29,), 54 (1992)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1994-03-24  

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