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2013 Fiscal Year Final Research Report

Applications of Renormalization Group Methods in Mathematical Sciences

Research Project

  • PDF
Project/Area Number 23540257
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Global analysis
Research InstitutionSetsunan University

Principal Investigator

ITO Keiichi  摂南大学, 理工学部, 教授 (50268489)

Co-Investigator(Kenkyū-buntansha) TERAMOTO Toshiaki  摂南大学, 理工学部, 教授 (40237011)
宮尾 忠宏  摂南大学, 理工学部, 講師 (20554421)
宮尾 忠宏  北海道大学, 自然科学研究科, 准教授 (20554421)
Co-Investigator(Renkei-kenkyūsha) TAMURA Hiroshi  金沢大学, 機械工学系, 教授 (80188440)
HIROKAWA Masao  岡山大学, 自然科学研究科, 教授 (70282788)
HIROSHIMA Funio  九州大学, 数理学研究科, 准教授 (00330358)
Project Period (FY) 2011 – 2013
Keywordsくりこみ群 / ミレニアム問題 / シグマ模型 / 格子ゲージ模型 / くりこみ群の流れ
Research Abstract

We applied the renormalization group methods to the longstanding problems (the so-called Millennium problems) in mathematical sciences which go back to the last century. We apply this method to solve the 2D O(N) symmetric spin model which is a prototype model of the gauge theory model. In this model, one needs to integrate over infinite variables which form a functional space. We find a set of subspaces (called flow) which dominate the integral. This enables us to solve the recursive integrals and obtain the final result.

  • Research Products

    (21 results)

All 2014 2013 2012 2011 Other

All Journal Article (12 results) Presentation (4 results) Book (4 results) Remarks (1 results)

  • [Journal Article] Absence of Phase Transitions in 2D O(N) Spin Models and Renormalization Group Analysis2014

    • Author(s)
      Keiichi R. Ito
    • Journal Title

      数理解析研究所講究録

      Volume: 1904号 Pages: 147-159

  • [Journal Article] On a linerized system arising in the study of viscous surface flow down an inclined plane2014

    • Author(s)
      Y.Teramoto, K.Tomoeda
    • Journal Title

      Annali dell'Univ. di Ferrara

  • [Journal Article] Heat convection of Compressible Viscous fluids, II2013

    • Author(s)
      T.Nishida, Y.Teramoto, M.Paruda
    • Journal Title

      Journal of Math. Fluid Mechanics

      Volume: Vol.15 Pages: 689-700

  • [Journal Article] Monotonicity of the Polaron Energy II2013

    • Author(s)
      T.Miyao
    • Journal Title

      J.Stat.Phys

      Volume: vol.153 Pages: 70-92

  • [Journal Article] Multiplicity of the Lowest Eigenvalues of non-commutative harmonic oscillator2013

    • Author(s)
      F.Hiroshima
    • Journal Title

      Kyushu J. Math

      Volume: Vol.67 Pages: 355-366

  • [Journal Article] Probabilistic representation and fall-off of bound state of relativistic Schroedinger operator of spin 1/22013

    • Author(s)
      F.Hiroshima
    • Journal Title

      Publ.RIMS Kyoto

      Volume: vol.49 Pages: 189-214

  • [Journal Article] Lieb-Thirring bound for Schroedinger operators with Bernstein functions of the Laplacian2012

    • Author(s)
      F.Hiroshima
    • Journal Title

      Commun.Stoch.Anal

      Volume: vol.6 Pages: 589-602

  • [Journal Article] Random Point Field Approach to Analysis of Anisotropic Bose Einstein Condensations2012

    • Author(s)
      H.Tamura, V.Zagrevnov
    • Journal Title

      Markov Processes and Relat. Fields

      Volume: vol.18 Pages: 473-530

  • [Journal Article] Absence of Phase Transitions in 2D O(N) Heisenberg Model2012

    • Author(s)
      Keiichi R. Ito
    • Journal Title

      数理解析研究所講究録

      Volume: 1805 号 Pages: 51-62

  • [Journal Article] Ground State properties of SSH Model2012

    • Author(s)
      T.Miyao
    • Journal Title

      J. Math.Phys

      Volume: vol.53 Pages: 095215

  • [Journal Article] Infrared Problem for the Nelson Model with Lieb-Thirring bound for Schroedinger operators with Bernstein functions of the Laplacian2012

    • Author(s)
      F.Hiroshima
    • Journal Title

      Commun.Stoch.Anal

      Volume: vol.6 Pages: 589-602

  • [Journal Article] Heat convection of Compressible Viscous fluids, I

    • Author(s)
      T.Nishida, Y.Teramoto, M.Paruda
    • Journal Title

      Journal of Math. Fluid Mechanics

      Volume: Vol.15 Pages: 525 - 536

  • [Presentation] Absence of Phase Transitions in Two-Dimensional O(N) Heisenberg model with large N2014

    • Author(s)
      K.R.Ito
    • Organizer
      Harvard University Physics Seminar
    • Place of Presentation
      Harvard University
    • Year and Date
      20140300
  • [Presentation] Millenium Problem, Study of 2D O(N) Spin model2013

    • Author(s)
      K.R.Ito
    • Organizer
      数理解析研究所研究集会
    • Year and Date
      20130900
  • [Presentation] Study of O(N) Spin Model by RG Method and absence of Phase Transition2013

    • Author(s)
      K.R.Ito
    • Organizer
      Helsinki University Physics Seminar
    • Place of Presentation
      Helsinki
    • Year and Date
      20130300
  • [Presentation]2012

    • Author(s)
      K.R.Ito
    • Organizer
      17th International Congress of Mathematical Physics
    • Place of Presentation
      Aalborg (Debmark)
    • Year and Date
      20120800
  • [Book] 数理物理学の方法 , ノイマンコレクション I ( 翻訳と解説 )2013

    • Author(s)
      伊東恵一, 一瀬孝, 岡本久, 他
    • Total Pages
      450
    • Publisher
      ちくま書房
  • [Book] Enhanced Binding in Quantum Field Theory, COE Lecture Note Vol.382012

    • Author(s)
      F.Hiroshima, H.Spohn, I.Sasaki, A.Sasakil
    • Publisher
      Kyushu University
  • [Book] 解析学と物理学 , 数理科学 No.5872012

    • Author(s)
      伊東恵一 , 編著
    • Publisher
      サイエンス社
  • [Book] 繰り込み群の数理科学における応用 , SGC ライブラリー , vol.812011

    • Author(s)
      伊東恵一
    • Total Pages
      148
    • Publisher
      サイエン社
  • [Remarks]

    • URL

      http://www.setsunan.ac.jp/mpg/

URL: 

Published: 2015-07-16  

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