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Anomalies in Gauge Theories and Related Phenomena

Research Project

Project/Area Number 01540249
Research Category

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

Allocation TypeSingle-year Grants
Research Field 核・宇宙線・素粒子
Research InstitutionOsaka University

Principal Investigator

SHIZUYA Ken-ichi  Osaka University, Department of Physics Associate Professor, 理学部, 助教授 (50154216)

Project Period (FY) 1989 – 1990
Project Status Completed (Fiscal Year 1990)
Budget Amount *help
¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1990: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1989: ¥1,600,000 (Direct Cost: ¥1,600,000)
KeywordsAnomalies / Chiral symmetry / Gauge theories / Charge density waves / Anyons / Kac-Moody algebra / Quantum Hall effect / High-T superconductivity / 端数粒子統計
Research Abstract

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

Report

(3 results)
  • 1990 Annual Research Report   Final Research Report Summary
  • 1989 Annual Research Report
  • Research Products

    (25 results)

All Other

All Publications (25 results)

  • [Publications] S.Miyake: "Noncanonical features in an anomalous gauge theory." Modern Physics Letters A. 4. 775-782 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] S.Miyake: "Consistent quantization of a chiral gauge theory in four dimensions." Modern Physics Letters A. 4. 2675-2683 (1989)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] B.Sakita: "Moving charge density waves without Peierls distortion in oneーdimensional coductors." Physics Letters A. 145. 209-213 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] B.Sakita: "Local chiral symmetry and charge density waves in oneーdimensional conductors." Physical Review B. 42. 5586-5593 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K.Shizuya: "Anyon statistics and its variation with wavelengths in MaxwellーChernーSimons gauge theories." Physics Letters B. 252. 412-416 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] S.Miyake: "Consistency and current algebras of a NonーAbelan chiral gauge theory in four dimensions"

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K.Shizuya: "Collective field theory for electrons in a magnetic field and the quantum Hall effect."

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 静谷 謙一: "量子異常(物理学最前線シリ-ズの一巻に掲載)" 共立出版株式会社, 60 (1991)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] S. Miyake: "Noncanonical features in an anomalous gauge theory." Modern Physics Letters. A4. 775-782 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] S. Miyake: "Consistent quantization of a chiral gauge theory in four dimensions" Modern Physics Letters. A4. 2675-2683 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] B. Sakita: "Moving charge density waves without Peierls distortion in one-dimensional conductors." Physics Letters. A145. 209-213 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] B. Sakita: "Local chiral symmetry and change density waves in one-dimensional conductors" Physical Review. B42. 5586-5593 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K. Shizuya: "Anyon statistics and its variation with wavelengths in Maxwell-Chern-Simons gauge theories." Physics Letters. B252. 412-416 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] S. Miyake: "Consistency and current algebras of a Non-Abelan chiral gauge theory in for dimensions." (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] K. Shizuya: "Collective field theory for electrons in a magnetic field and the quantum Hall effect." (1991)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Bunji Sakita: "Moving charge density waves without Peierls distortion in oneーdimensional conductors." Physics Letters A. 145. 209-213 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Bunji Sakita: "Local Chiral symmetry and charge density waves in oneーdimensional conductors." Physical Review B. 42. 5586-5593 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Kenーichi Shizuya: "Anyon statistics and its variation with wavelengths in MaxwellーChernーSimons gauge theories." Physics Letters B. 252. 412-416 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] Shogo Miyake: "Consistency and current algebras of a NonーAbelan chiral gauge theory in four dimensions" (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Kenーichi Shizuya: "Collective field theory for electrons in a magnetic field and the quantum Hall effect." (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] 静谷 謙一: "量子異常(物理学最前線シリ-ズ 一巻)" 共立出版株式会社, 60 (1991)

    • Related Report
      1990 Annual Research Report
  • [Publications] Kenーichi Shizuya: "Consistent quantization and symmetry structure of a nonーAbelian chiral qauge theory." Physical Review D. 40. 1260-1267 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Shogo Miyake: "Noncanonical features in an anomalous gauge theory." Modern Physics Letters A. 4. 775-782 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Shogo Miyake: "Consistent quantization of a chiral gauge theory in four dimensions." Modern Physics Letters A. 4. 2675-2683 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] Bunji Sakita: "Moving charge density waves without Peierls'distortion in oneーdimensional conductors." Physics Letters A. (1990)

    • Related Report
      1989 Annual Research Report

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Published: 1989-04-01   Modified: 2016-04-21  

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