• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Deformation quantization and noncommutative geometry

Research Project

Project/Area Number 15540094
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTokyo University of Science

Principal Investigator

YOSHIOKIA Akira  Tokyo University of Science, Department of Mathematics Faculty of Science, Professor, 理学部, 教授 (40200935)

Co-Investigator(Kenkyū-buntansha) OMORI Hideki  Tokyo University of Science, Department of Mathematics Faculty of Science and Technology, Professor, 理工学部, 教授 (20087018)
HARA Tamio  Tokyo University of Science, Department of Mathematics Faculty of engineering, Professor, 工学部, 教授 (10120205)
MAEDA Yoshiaki  Keio University, Department of mathematical science, Faculty of Science and Technology, Professor, 理工学部, 教授 (40101076)
MIYAZAKI Naoya  Keio University, Department of Mathematics, Faculty of Economics, Assistant Professor, 経済学部, 助教授 (50315826)
Project Period (FY) 2003 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2004: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2003: ¥2,000,000 (Direct Cost: ¥2,000,000)
KeywordsDeformation quantization / Star product / Symplectic geometry / Quantization / Hamiltonian mechanics / Hamiltonian mechanics / gerbe / Lie group / Deformation Quantization / gerb / Deformation quantizalion / Hamiltonia mechanics
Research Abstract

By means of a complex symmetric matrix K, we have a linear isomorphism from the Weyl algebra to the space of all polynomial P(C,2n). We introduce a topology into the space P(C,2n) with respect to which the induced product is smooth, and we can take the completion. The star exponential belongs to the complete space. We investigate the two constructions of the star exponential function of the quadratic forms in P(C,2n). One is given by the path integral methods and the other is given by solving an ordinary differential equation. We investiageted the associated bundle structure over the space of symmetric matrices. We also investigate the noncommutative complex projective space given by convergent star products. In future we will study the extended concept of bundle structure which naturally enters through convergent star product algebras.

Report

(3 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • Research Products

    (35 results)

All 2005 2004 2003 Other

All Journal Article (23 results) Book (5 results) Publications (7 results)

  • [Journal Article] Star exponential functions as two-valued elements2005

    • Author(s)
      Yoshiaki Maeda
    • Journal Title

      Progress in Mathematics 232

      Pages: 483-492

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Classification of all quadratic star product on a plane2005

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      Lecture Notes in Physics 662

      Pages: 113-126

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Universal Deformation Formulae for Three-Dimensional Solvable Lie groups2005

    • Author(s)
      Pierre Bieliavsky
    • Journal Title

      Lecture Notes in Physics 662

      Pages: 127-142

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Star exponential functions as two-valued elements2005

    • Author(s)
      Yoshiaki Maeda, Naoya Miyazaki, Hideki Omori, Akira Yoshioka
    • Journal Title

      Progress in Mathematics 232

      Pages: 483-492

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] On G-fiberings over the circle within a cobordism class2004

    • Author(s)
      Tamio Hara
    • Journal Title

      Kodai Mathematical Journal 27

      Pages: 30-44

    • NAID

      130003574445

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Contact Weyl manifoldにおける指数定理とrepresentable K-theory2004

    • Author(s)
      宮崎 直哉
    • Journal Title

      数理解析研究所講究録 1408

      Pages: 40-60

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Index Theorem in Contact Weyl manifold and representable K-theory2004

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      Suuriken Kohkyuroku 1408

      Pages: 40-60

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Path integral for star exponential functions of quadratic forms2003

    • Author(s)
      Akira Yoshioka
    • Journal Title

      Geometry, Integrability and Quantization, I. Mladenov G. Naber ed. 4

      Pages: 330-340

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Strange phenomena related to ordering problems2003

    • Author(s)
      Hideki Omori
    • Journal Title

      Journal of Lie Theory 13

      Pages: 481-510

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] String theories and deformation quantization2003

    • Author(s)
      Yoshiaki Maeda
    • Journal Title

      Suugaku 55

      Pages: 245-265

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On a construction of a good parametrix for the Pauli equation by Hamiltonian path-integral method. An application of super analysis2003

    • Author(s)
      Atushi Inoue
    • Journal Title

      Japanese Journal of Mathematics 29

      Pages: 27-107

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Deformation quantization and noncommutative differential geometry2003

    • Author(s)
      Yoshiaki Maeda
    • Journal Title

      Sugaku Expositions 16

      Pages: 1-23

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Multiplicative SK invariants on Z_n manifolds with boundary2003

    • Author(s)
      Tamio Hara
    • Journal Title

      Rocky Mountain Journal of Mathematics 33

      Pages: 875-901

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Multiplicative SK invariants for closed Z2r manifolds2003

    • Author(s)
      Tamio Hara
    • Journal Title

      Kyushyu Journal of Math 57

      Pages: 227-253

    • NAID

      110001263198

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Multiplicative SK invariants for G manifolds with boundary2003

    • Author(s)
      Tamio Hara
    • Journal Title

      Tokyo J. of Math. 26

      Pages: 261-273

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Path integral for star exponential functions of quadratic forms2003

    • Author(s)
      Akira Yoshioka
    • Journal Title

      Geometry, Integrability and Quantization(I.Mladenov G.Naber ed.) 4

      Pages: 330-340

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Strange phenomena related to ordering problems2003

    • Author(s)
      Hideki Omori et al.
    • Journal Title

      Journal of Lie Theory 13

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Deformation quantization and noncommutative differential Geometry2003

    • Author(s)
      Yoshiaki Maeda
    • Journal Title

      Sugaku Expositions 16

      Pages: 1-23

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Multiplicative SK invariants for G manifolds with boundary2003

    • Author(s)
      Tamio Hara
    • Journal Title

      Tokyo J.of Math. 26

      Pages: 261-273

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On vectorial gerbes and Poincare-Cartan classes

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      Proceedings in Noncommutative geometry and Physics (World Scientific) (To appear)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Universal Deformation Formulae for Three-Dimensional Solvable Lie groups

    • Author(s)
      Pierre Bieliavsky, Philippe Bonneau, Yoshiaki Maeda
    • Journal Title

      Lecture Notes in Physics 662

      Pages: 127-142

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On vectorial gerbes and Poincare-Cartan classes

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      Proceedings in Noncommutative geometry and Physics (World Scientific) (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On vectorial gerbes and Poincare-Cartan classes

    • Author(s)
      Naoya Miyazaki
    • Journal Title

      Proceedings of Noncommutative geometry and Mathematical Physics (World Scientific) (tentative title)(To appear)

    • Related Report
      2004 Annual Research Report
  • [Book] 量子的な微分積分2005

    • Author(s)
      大森 英樹
    • Total Pages
      376
    • Publisher
      シュプリンガーフェアラーク東京
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Book] Quantum Field theory and noncommutative geometry, Lecture Notes in Physics 6622005

    • Author(s)
      Ursula Carow-Watamura
    • Total Pages
      300
    • Publisher
      Springer
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Book] Lecture notes in Physics, vol.6622005

    • Author(s)
      Carow-Watamura, Ursula, Maeda, Yoshiaki, Watamura, Satoshi (ed)
    • Total Pages
      297
    • Related Report
      2004 Annual Research Report
  • [Book] 数学のなかの物理学2004

    • Author(s)
      大森 英樹
    • Total Pages
      343
    • Publisher
      東大出版会
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Book] 量子的な微分積分2004

    • Author(s)
      大森 英樹, 前田 吉昭
    • Total Pages
      337
    • Publisher
      シュプリンガーフェアラーク東京
    • Related Report
      2004 Annual Research Report
  • [Publications] A.Yoshioka, T.Matsumoto: "Path integral star exponential functions of quadratic forms"Geometry, Integrability and Quantization, I.Mladenov G.Naber ed.. 4. 330-340 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Omori, Y.Maeda, N.Miyazaki, A.Yoshioka: "Strange Phenomena rekated ti ordering problems in quantization"Journal of Lie Theory. 13. 481-510 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Hara: "Multiplicative SK invariants for closed Z2r manifolds"Kyushyu J.of Math.. 57. 227-253 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Hara: "Multiplicative SK invariants on Zn manifolds with boudary"Rockey Mountain J.of Math.. 33. 875-901 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Hara: "Multiplicative SK invariants for G manifolds with boundary"Tokyo J.of Math. 26. 261-273 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Omori, Y.Maeda, N.Miyazaki, A.Yoshioka: "Star exponential functions as two-valued elements"Proceedings, in honor of Alan Weinstein, Birkhauser. (To appear).

    • Related Report
      2003 Annual Research Report
  • [Publications] 大森 英樹, 前田 吉昭: "量子的な微分積分"シュプリンガーフェアラーク東京(出版予定). 376 (2004)

    • Related Report
      2003 Annual Research Report

URL: 

Published: 2003-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi