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The method of the Riemann-Hilbert problem for singular phenomenas in mathematical physics

Research Project

Project/Area Number 12640222
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionNihon University

Principal Investigator

SUZUKI Osamu  Department of Comuter and System Analysis, College of Humanities and Sciences, Nihon University, professor, 文理学部, 教授 (10096844)

Project Period (FY) 2000 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2001: ¥600,000 (Direct Cost: ¥600,000)
KeywordsThe method of the Riemann-Hilbert problems / Dimension regularization, Pauli-Vilaars regularization / anomaly / quarkconfinement / fractal geometry / abelianization theory / Infinte dimensional Cliffor algebras / Cuntz algebra / Riemann-Hilbert問題 / くりこみ理論 / 正則化
Research Abstract

Singular phenomenas are investigated by use of the method of the Riemann-Hilbert problems. The following three topics are treated :
(1) The problems of divergence in quantum field theory are discussed. The method of the Riemann-Hilbert problems supply the canonical forms of the divergences in local. Hence we can divide the divergence by the canonical one and we can get the vector bundle associated to the divergences. The anomaly can be described in terms of the characteristic classes of the bundle, which can be imeadiatlly obtained through the Fuchs relations.
(2) The quarkconfinement can be discussed by use of the Riemann-Hilbert problems. After the formulation of the A belianization method, we can obtain the singular fieilds and the singular gauge trasformations. Then we can formulate the Riemann-Hilbert problems for the singularities and we can get the non-trivial anomaly which gives the mass of the gluons. Following the discussions in the Meissner effects, we can gent the quarkconfinement.
(3) Toward the Riemann-Hilbert problem for non pertubative field theory. It is expected that non-pertabative method will be necessary for the real field theory. Here we prepare fundamental materials for this purpose. We treat the fractal geometry and discuss the sigularities by use of the algebraic method. Namely we consider the representations of the Cuntz algebras and discuss the infinite dimensional (Clifford algebras and the periodicity theorems in them.

Report

(3 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • Research Products

    (27 results)

All Other

All Publications (27 results)

  • [Publications] Osamu SUZUKI, A.Asada: "The Riemann-Hilbert problem for a higher dimensional homology group on a real manifold"Proc.of the Int.Conf.on Boud.Valu.Probl.Int.Equ.and related Problems(World.Scientific). 23-33 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI, A.Asada: "The vertex operators in the string theory and Lauricella hypergeometric functions"Bul.de la Soc.de Scie.Et des letter de Lodz, Recherches sur les Deformations. XXXI. 127-134 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI, A.Asada: "A mathematical approach to the SU(2)-quark confinement"Proc.of Int.Sym.on Quantum Chromodyn.and Color Confin.(Confinemnt 2000)(World Scientific). 379-382 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI, J.Lawrynowicz: "An Introduction to Pseudotwistors : Spinor Solutions vs.Harmonic Forms and Cohomology Groups"Clifford Algebras and their Applications in Mathematical Physics Vol.1:Algebra and Physics(Birchhauser). 393-423 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI, J.Lawrynowicz: "An Introduction to pseudotwistors : spinor equations"Rev.Roum.Math.Pure and Appl.. 46. 56-65 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI, J.Lawrynowicz: "Psuedotwistors"Int.Jour.Of Theo.Phys.. 40. 387-397 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI (with A.Asada): "The Riemaim-Hilbert problems for a higher dimensional homology group on a real manifold"Proc. of the Int. Cof. on boundary value problems and related topics, World Scientific. 23-33 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI (with A.Asada): "The vertex operators in the string field theory and Lauriccela hypergeometric functionfunctions"Bul. De. la Soc. Des letter de Lodz Res. Sur les Deform.. XXXI. 127-134 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI (with A.Asada): "A mathematical approach to the SU(2) - quarkconfinement"Proc. Int. Symm. Quarkconfinement(Quarkconfinement 2000, World Scientific). 379-382 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI (with J.Lawrynowicz): "An introduction to pseudotwistors : Spinor solutions vs. harmonic forms and cohomology groups"Clifford algebras and their application in mathematical physics, Vol. 1 : Algebras and Physics, Birchhauser. 382-393 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI (with J.Lawrynowicz): "An introduction to pseudotwistors, Spinor equations"Rev. Roum. Math. Pure and Appl.. 56-65 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI (with J.Lawrynowicz): "An introduction to pseudotwistors ; Basic constructions"Quaternic strucuturesin mathematical physics (World Scientific). 241-252 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI (with J.Lawrynowicz): "Pseudotwistors"Int. Jour. Theo. Phys.. 387-297 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI (with J.Lawrynowicz): "Hurwitz-type and space-time-type duality theorems for Hermitian Hurwitz pairs"Oerator theory, Advances and Applications, Vol. 114(Birkhauser). 155-169 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI (with J.Lawrynowicz): "An approach to the 5-, 9-, and 13-dimensional complex dynamics III"Bul. De la Soc. Des letter de Lodz Res. Sur les Deform. XXXIV. 91-119 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI (with J.Lawrynowicz): "From order surface pheomena to graded fractal bundles related to complex and Pauli structures"Bul. De la Soc. Des letter de Lodz Res. Sur les Deform. XXXV. 67-98 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI with J.Lawrynowicz, K.Nono, N.Fujimoto): "A basic construction of real Hurwitz pairs"Bul. De la Soc. Des letter de Lodz Res. Sur les Deform. XXXIV. 77-89 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI with J.Lawrynowicz, K.Nono, N.Fujimoto): "An explicit construction of real Hurwitz pairs"To appear in the Proc. of the 3th-ISSAC Int. Conference in Berlin. (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI (with M.Mori and Y.Watatani): "A noncommutative differential geometrical method to fractal geometry(Representations of Cuntz algebras of Hausdorff type on self similar fractal sets)"To appear in the Proc. of the 3th-ISSAC Int. Conference in Berlin. (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Osamu SUZUKI(with A.Asada): "The Riemann-Hilbert problem for a higher dimensional homology group on a real manifold"Proc.of the Int.Conf.on Boud.Valu.Probl.Int.Equ.and related Problems(World.Scientific).. 23-33 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Osamu SUZUKI(with A.Asada): "The vertex operators in the string theory and Lauricella hypergeometric functions"Bul.de la Soc.de Scie.Et des letter de Lodz,Recherches sur les Deformations. XXXI. 127-134 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Osamu SUZUKI(with A.Asada): "A mathematical approach to the SU(2)-quark confinement"Proc.of Int.Sym.on Quantum Chromodyn.and Color Confin.(Confinement 2000)(World Scientific). 379-382 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Osamu SUZUKI(with J.Lawrynowicz): "An Introduction to Pseudotwistors:Spinor Solutions vs.Harmonic Forms and Cohomology Groups"Clifford Algebras and their Applications in Mathematical Physics Vol.1:Algebra and Physics(Birchhauser). 393-423 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Osamu SUZUKI(with J.Lawrynowicz): "An Introduction to pseudotwistors spinor equations"Rev.Roum.Math.Pure and Appl.. 46. 56-65 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] Osamu SUZUKI(with J.Lawrynowicz): "Psuedotwistors"Int.Jour.Of Theo.Phys.. 40. 387-397 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] O.Suzuki(with J.tawrynowicz): "Pseudotwistors"Int.Jour.of Theoretical Physics. 40. 383-393 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] O.Suzuki(with J.tawrynowicz): "Hurwitz-type and space-time duality theorems for Hermitian Hurwitz Pairs"Operator theory : Adrances and Applications. 114. 156-169 (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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