{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1040282256563014656.json","@type":"Project","projectIdentifier":[{"@type":"KAKEN","@value":"03640273"},{"@type":"JGN","@value":"JP03640273"},{"@type":"URI","@value":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03640273/"}],"jpcoar:awardTitle":[{"@language":"ja","@value":"ゲージ理論の物性物理への応用"},{"@language":"en","@value":"Applications of Gauge Theories to Condensed-Matter Physics"}],"field":[{"keyword":[{"language":"ja","textList":["理学","物理学","核・宇宙線・素粒子"]},{"language":"en","textList":["Science","Physics","核・宇宙線・素粒子"]}]}],"dc:language":"ja","description":[{"type":"abstract","notation":[{"@language":"ja","@value":"対称性は保存則と密接な関係をもっており,対称性の観点から物理現象を把握することは重要である。特に.超伝導や超流動のような巨視的なスケールで起こる量子力学的輸送現象は力学系の対称性との関わりが深く.その記述にゲージ理論が有効に適用できる場合も少なくない。この事実を踏まえ.平成3年と4年の2年度に渡り.量子ホール効果をゲージ理論の見地から研究するとともにゲージ場の幾何学的属性に由来する諸現象(量子異常.アハロノフ.ボーム効果など)を考察した。その内容は以下の通りである。\n1.磁場中の電子を記述する集団場理論を構築して.整数量子ホール効果をゲージ不変性との関連で考察した。ホール伝導度が不純物ポテンシャルの影響を受けない一種の断熱不変量であることを示して.その量子化の精度が著しく高い事実を説明した。さらに.この理論を拡張して.有限のホール電子系の端を流れる電流の力学を考察した。局在が原因となって系の端を流れるホール電流の描像が得られることを指摘する論文を最近発表した。\n2.整数および分数量子ホール効果との関連から.量子効果としてチャーン.サイモン項が誘導される機構に関心が持たれている。この現象は外電磁場に対する量子的な真空(ディラックの海)の応答として物理的な観点から理解できることを示す論文を現在準備している。\n3.アハロノフ・ボーム効果.アハロノフ・キャッシャー効果が電磁場の角運動量と密接に関係していることを指摘する論文を投稿中である。\n4.量子異常の起源と役割を探るために異常項を持つゲージ理論の研究を続けてきたが.この2年間で考察を4次元の非可換ゲージ理論にまで進めた。従来よりゲージ理論の枠組みが広がることを確認するとともに.ゲージ理論の代数的構造を通してゲージ異常項とシュビンガー項が密接に結びついていることを明確に示した。"},{"@language":"en","@value":"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.).\n1. 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.\n2. 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.\n3. A paper pointing out that the Aharonov-Bohm and Aharonov-Casher effects are tied to electromagnetic angular momentum was presented.\n4. 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."}]}],"researcher":[{"@id":"https://cir.nii.ac.jp/crid/1420845751151373824","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"50154216"},{"@type":"NRID","@value":"1000050154216"},{"@type":"NRID","@value":"9000018320249"},{"@type":"NRID","@value":"9000003197710"},{"@type":"NRID","@value":"9000247079271"},{"@type":"NRID","@value":"9000003408779"},{"@type":"NRID","@value":"9000003391516"},{"@type":"NRID","@value":"9000005823114"},{"@type":"NRID","@value":"9000364879886"},{"@type":"NRID","@value":"9000364889292"},{"@type":"NRID","@value":"9000277508783"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/read0012435"}],"foaf:name":[{"@language":"ja","@value":"静谷 謙一"},{"@language":"en","@value":"SHIZUYA Kenichi"}],"jpcoar:affiliationName":[{"@language":"ja","@value":"京都大学"},{"@language":"en","@value":"Yukawa Inst. for Theor. Phys.,Kyoto University,Professor"}],"role":"principal_investigator"}],"since":"1991","until":"1992","institution":[{"institutionIdentifier":[{"@type":"NII","@value":"0014301"}],"notation":[{"@language":"ja","@value":"京都大学"},{"@language":"en","@value":"KYOTO UNIVERSITY"}]},{"institutionIdentifier":[{"@type":"NII","@value":"0014401"}],"notation":[{"@language":"ja","@value":"大阪大学"},{"@language":"en","@value":"Osaka University"}]}],"fundingProgram":[{"jpcoar:funderName":[{"@language":"ja","@value":"科学研究費助成事業"},{"@language":"en","@value":"Grants-in-Aid for Scientific Research"}]}],"url":[{"@id":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03640273/","notation":[{"@value":"KAKEN"}]}],"createdAt":"1991-03-31","modifiedAt":"2025-11-19","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=%E3%82%B2%E3%83%BC%E3%82%B8%E7%90%86%E8%AB%96","dc:title":"ゲージ理論"},{"@id":"https://cir.nii.ac.jp/all?q=%E5%AF%BE%E7%A7%B0%E6%80%A7","dc:title":"対称性"},{"@id":"https://cir.nii.ac.jp/all?q=%E9%87%8F%E5%AD%90%E7%95%B0%E5%B8%B8","dc:title":"量子異常"},{"@id":"https://cir.nii.ac.jp/all?q=%E9%87%8F%E5%AD%90%E3%83%9B%E3%83%BC%E3%83%AB%E5%8A%B9%E6%9E%9C","dc:title":"量子ホール効果"},{"@id":"https://cir.nii.ac.jp/all?q=%E7%AB%AF%E9%9B%BB%E6%B5%81","dc:title":"端電流"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%82%A2%E3%83%8F%E3%83%AD%E3%83%8E%E3%83%95%E3%83%BB%E3%83%9C%E3%83%BC%E3%83%A0%E5%8A%B9%E6%9E%9C","dc:title":"アハロノフ・ボーム効果"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%82%A2%E3%83%8F%E3%83%AD%E3%83%8E%E3%83%95%E3%83%BB%E3%82%AD%E3%83%A3%E3%83%83%E3%82%B7%E3%83%A3%E3%83%BC%E5%8A%B9%E6%9E%9C","dc:title":"アハロノフ・キャッシャー効果"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%82%B2-%E3%82%B8%E7%90%86%E8%AB%96","dc:title":"ゲ-ジ理論"},{"@id":"https://cir.nii.ac.jp/all?q=%E9%87%8F%E5%AD%90%E3%83%9B-%E3%83%AB%E5%8A%B9%E6%9E%9C","dc:title":"量子ホ-ル効果"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%83%95%E3%82%A7%E3%83%AB%E3%83%9F%E7%B5%B1%E8%A8%88","dc:title":"フェルミ統計"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%82%A2%E3%83%8F%E3%83%AD%E3%83%8E%E3%83%95%E3%83%BB%E3%83%9C-%E3%83%A0%E5%8A%B9%E6%9E%9C","dc:title":"アハロノフ・ボ-ム効果"},{"@id":"https://cir.nii.ac.jp/all?q=%E3%82%A2%E3%83%8F%E3%83%AD%E3%83%8E%E3%83%95%E3%83%BB%E3%82%AD%E3%83%A3%E3%83%83%E3%82%B7%E3%83%A3-%E5%8A%B9%E6%9E%9C","dc:title":"アハロノフ・キャッシャ-効果"},{"@id":"https://cir.nii.ac.jp/all?q=Gauge%20theories","dc:title":"Gauge theories"},{"@id":"https://cir.nii.ac.jp/all?q=Symmetry","dc:title":"Symmetry"},{"@id":"https://cir.nii.ac.jp/all?q=Anomalies","dc:title":"Anomalies"},{"@id":"https://cir.nii.ac.jp/all?q=Quantum%20Hall%20effect","dc:title":"Quantum Hall effect"},{"@id":"https://cir.nii.ac.jp/all?q=Edge%20current","dc:title":"Edge current"},{"@id":"https://cir.nii.ac.jp/all?q=Aharonov-Bohm%20effect","dc:title":"Aharonov-Bohm effect"},{"@id":"https://cir.nii.ac.jp/all?q=Aharonov-Casher%20effect","dc:title":"Aharonov-Casher effect"}],"dataSourceIdentifier":[{"@type":"KAKEN","@value":"03640273"}],"grant":{"grantIdentifier":[{"@type":"NII","@value":"14"}],"jpcoar:fundingStream":[{"@language":"ja","@value":"一般研究(C)"},{"@language":"en","@value":"Grant-in-Aid for General Scientific Research (C)"}]},"allocationClassification":[{"notation":[{"@language":"ja","@value":"補助金"},{"@language":"en","@value":"Single-year Grants"}]}],"projectStatus":"project_closed","allocationAmount":{"totalCost":{"amount":"1300000","currency":"JPY"},"breakdownCost":[{"notation":[{"@language":"ja","@value":"直接経費"},{"@language":"en","@value":"Direct Cost"}],"amount":"1300000","currency":"JPY"}]}}