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2005 Fiscal Year Final Research Report Summary

Research on Operator Analysis for Nonrelativistic Quantum Dynamics in High Energy Region

Research Project

Project/Area Number 16540155
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOKAYAMA UNIVERSITY

Principal Investigator

HIROKAWA Masao  Okayama Univ., Grad.Sch.Nat.& Tech., Professor, 大学院・自然科学研究科, 教授 (70282788)

Co-Investigator(Kenkyū-buntansha) HIROSHIMA Fumio  Kyushu Univ., Fac.Math., Associate Professor, 大学院・数理学研究院, 助教授 (00330358)
TAMURA Hideo  Okayama Univ., Grad.Sch.Nat.& Tech., Professor, 大学院・自然科学研究科, 教授 (30022734)
SATO Ryotaro  Okayama Univ., Grad.Sch.Nat.& Tech., Professor, 大学院・自然科学研究科, 教授 (50077913)
TANAKA Katsumi  Okayama Univ., Admission center, Associate Professor, アドミッションセンター, 助教授 (60207082)
Project Period (FY) 2004 – 2005
KeywordsNonrelativistic QED / Operator Analysis / Ultraviolet Cutoff
Research Abstract

There are some mathematical problems in nonrelativistic quantum electrodynamics. Especially, we have been concerned with ultraviolet catastrophe in high energy region and moreover infrared catastrophe after removing ultraviolet cutoff.
Hirokawa established some problems on ultraviolet catastrophe and/or infrared castastrophe in mathematics. Hiroshima and Spohn investigated the renormalized mass of electron. Hirokawa, Hiroshima, and Spohn have succeeded in removing both, ultraviolet and infrared cutoffs for the so-called Nelson model, which describes the electron coupled with photons in such as hydrogen-like atom. Also, Hirokawa clarified that the result by the regular perturbation theory is still available in the above model after removing both cutoffs in collaboration with Hainzl and Spohn. They employed a nonperturbative method to prove it.
Hirokawa studied scattering theory with Tamura, problem on singularity of ultraviolet catastrophe with Tanaka, and uniqueness of the ground state with Sato.

  • Research Products

    (12 results)

All 2005 2004

All Journal Article (12 results)

  • [Journal Article] Ground State for Point Particles Interacting Through a Massless Scalar Bose Field2005

    • Author(s)
      M.Hirokawa
    • Journal Title

      Adv. Math. 191・2

      Pages: 339-392

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Binding Energy for Hydrogen-Like Atoms in the Nelson Model without Cutoffs2005

    • Author(s)
      C.Hainzl
    • Journal Title

      J. Funct. Anal. 220・2

      Pages: 424-459

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] On the range of a closed operator in an $Lsb 1$-space of vector-valued functions2005

    • Author(s)
      R.Sato
    • Journal Title

      Comment. Math. Univ. Carolin. 46

      Pages: 349-367

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Ground State for Point Particles Interacting Through a Massless Scalar Bose Field2005

    • Author(s)
      M.Hirokawa
    • Journal Title

      Adv.Math. 191・2

      Pages: 339-392

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Binding Energy for Hydrogen-Like Atoms in the Nelson Model without Cutoffs2005

    • Author(s)
      C.Hainzl
    • Journal Title

      J.Funct.Anal. 220・2

      Pages: 424-459

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On the range of a closed operator in an $Lsb 1$-space of vector-valued functions2005

    • Author(s)
      R.Sato
    • Journal Title

      Comment.Math.Univ.Carolin. 46

      Pages: 349-367

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] A model of interband radiative transition2004

    • Author(s)
      J.Dittrich
    • Journal Title

      J. Math. Soc. Japan 56・3

      Pages: 753-786

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Solvability of the functional equation f=(T-I)h for vector-valued functions2004

    • Author(s)
      R.Sato
    • Journal Title

      Colloq. Math. 99・2

      Pages: 253-265

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Scattering of Dirac particles by electromagnetic fields with small support in two dimensions and effect from scalar potentials2004

    • Author(s)
      H.Tamura
    • Journal Title

      Ann. Henri Poincare 5・1

      Pages: 75-118

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A model of interband radiative transition2004

    • Author(s)
      J.Dittrich, et al.
    • Journal Title

      J.Math.Soc.Japan 56・3

      Pages: 753-786

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Solvability of the functional equation f=(T-I)h for vector-valued functions2004

    • Author(s)
      R.Sato
    • Journal Title

      Colloq.Math. 99・2

      Pages: 253-265

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Scattering of Dirac particles by electromagnetic fields with small support in two dimensions and effect from scalar potentials2004

    • Author(s)
      H.Tamura
    • Journal Title

      Ann.Henri Poincare 5・1

      Pages: 75-118

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

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Published: 2007-12-13  

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