Infinite-Dimensional Stochastic approach to Geometrical Objects

• Project/Area Number: 17540124
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Saga University
• Principal Investigator: MITOMA Itaru Saga University, Mathematics, Professor, 理工学部, 教授 (40112289)
• Co-Investigator(Kenkyū-buntansha): OGURA Yukio Saga University, Mathematics, Professor, 理工学部, 教授 (00037847) ; TANIGUCHI Setsuo Kyushu University, Mathematics, Professor, 大学院・数理学研究院, 教授 (70155208) ; ICHIKAWA Takashi Saga University, Mathematics, Professor, 理工学部, 教授 (20201923) ; AIDA Shigeki Osaka University, Mathematics, Professor, 大学院・基礎工学研究科, 教授 (90222455) ; HANDA Kenji Saga University, Mathematics, Associate Professor, 理工学部, 助教授 (10238214)
• Project Period (FY): 2005 – 2006
• Project Status: Completed (Fiscal Year 2006)
• Budget Amount: ¥3,200,000 (Direct Cost: ¥3,200,000); Fiscal Year 2006: ¥1,500,000 (Direct Cost: ¥1,500,000); Fiscal Year 2005: ¥1,700,000 (Direct Cost: ¥1,700,000)
• Keywords: Chern-Simons integral / Wiener space / Wilson line / Holonomy / Topological invariant / Topological field theory / Superstring / Wiener空間 / リンク不変量 / 漸近展開 / チャーン・サイモンズ理論 / ウィルソンループ / リンク数 / ファインマン積分

Research Abstract

We,(Mitoma-Nishikawa),gave a mathematical definition for perturbative 1-loop approximation of the Chern-Simons integral with respect to the Wilson lines in an abstract Wiener space setting and proved the asymptotic expansion theorem. Further we calculate the copefficients for 3-dimensional surface and obtained link invariants. The result is now prepared for submission. We,(Albeverio-Mitoma),gave mathematical definitions for finite part and asymptotic estimate for infinite part of perturbative Chern-Simons integral via Wiener space. The result is appeared in SFB,611 in Bonn University.

Research Products

• [Journal Article] Asymptotic Expansion of Perturbative Chern-Simons Theory Via Wiener Space (2007)
  • Author(s): S.Albeverio, I.Mitoma
  • Journal Title: SFB 611, Bonn University No. 322 Pages: 50-50
  • Description: 「研究成果報告書概要(和文)」より
• [Journal Article] Asymptotic Expansion of Perturbative Chern-Simons Theory via Wiener Space (2007)
  • Author(s): Sergio Albeverio, Itaru Mitoma
  • Journal Title: SFB 611, Bonn University No. 322 Pages: 50-50
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Asymptotic Expansion of Perturbative Chern-Simons Theory via Wiener Space (2007)
  • Author(s): Sergio Albeverio, Itaru Mitoma
  • Journal Title: SFB611, Bonn University 322 Pages: 50-50
• [Journal Article] On a Choquet theorem for random upper semicontinuous functions (2006)
  • Author(s): Yukio Ogura
  • Journal Title: Soft Method for Integrated Uncertainty Modelling Pages: 145-151
  • Description: 「研究成果報告書概要(和文)」より
• [Journal Article] Strong law of large numbers for independent fuzzy set-valued random variables (2006)
  • Author(s): Shoumei Li, Yukio Ogura
  • Journal Title: Fuzzy Sets and Systems 157 Pages: 2569-2578
  • Description: 「研究成果報告書概要(和文)」より
• [Journal Article] On the Quadratic Wiener Functional Associated with the Malliavin Derivative of the Square Norm of Brownian Sample Path on Interval (2006)
  • Author(s): Setsuo Taniguchi
  • Journal Title: Electron. Comm. Probab. 11 Pages: 1-10
  • Description: 「研究成果報告書概要(和文)」より
• [Journal Article] Brownian sheet and reflectionless potentials (2006)
  • Author(s): Setsuo Taniguchi
  • Journal Title: Stoch. Pro. Appl. 116 (2) Pages: 293-309
  • Description: 「研究成果報告書概要(和文)」より
• [Journal Article] A family of Schottky groups arising from the hypergeometric equation (2006)
  • Author(s): Takashi Ichikawa, Masaaki Yoshida
  • Journal Title: Proc. of Amer. Math. Soc 134 (8) Pages: 2271-2280
  • Description: 「研究成果報告書概要(和文)」より
• [Journal Article] A note on random upper semicontinuous functions (2006)
  • Author(s): Hung T.Nguen, Yukio Ogura, Santi Tasena, Hien Tran
  • Journal Title: Soft Method for Integrated Uncertainty Modelling Pages: 129-135
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Strong law of large numbers for independent fuzzy set-valued random variables (2006)
  • Author(s): Shoumei Li, Yukio Ogura
  • Journal Title: Fuzzy Sets and Systems Vol. 157 Pages: 2569-2578
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] On the Quadratic Wiener Functional Associated with the Malliavin Derivative of the Square Norm of Brownian Sample Path on Interval (2006)
  • Author(s): S.Taniguchi
  • Journal Title: Electron. Comm. Probab. 11 Pages: 1-10
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Brownian sheet and reflectionless potentials (2006)
  • Author(s): S.Taniguchi
  • Journal Title: Stoch. Pro. Appl. 116 (2) Pages: 293-309
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] A family of Schottky groups arising from the hypergeometric equation (2006)
  • Author(s): Takashi Ichikawa, Masaaki Yoshida
  • Journal Title: Proc. of Amer. Math. Soc. 134 (8) Pages: 2271-2280
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] Strong law of large numbers for independent fuzzy set-valued random variables (2006)
  • Author(s): Shoumei Li, Yukio Ogura
  • Journal Title: Fuzzy Sets and System 157 Pages: 2569-2578
• [Journal Article] Brownian sheet and reflectionless potientials (2006)
  • Author(s): Setsuo Taniguchi
  • Journal Title: Stoch. Pro. Appl. 116(2) Pages: 293-309
• [Journal Article] A family of Schottky groups arising from the hypergeometric equation, (2006)
  • Author(s): Takashi Ichikawa, Masaaki Yoshida
  • Journal Title: Proc. of Amer. Math. Soc. 134 (8) Pages: 2271-2280
• [Journal Article] Sampling formulae for symmetric selection (2005)
  • Author(s): Kenji Handa
  • Journal Title: Electron. Commun. Probab. 10 Pages: 223-234
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] On Some Metrics Compatible with the Fell-Matheron Topology
  • Author(s): Yukio Ogura
  • Journal Title: Internat. Jour. Approximate Reasoning (to appear)
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] On a class of one-dimensional Markov processes with continuous paths
  • Author(s): Nubuyuki Ikeda, Yukio Ogura
  • Journal Title: "Stochastic Analysis and Partial Differential Equations" AMS Comtemp. Math. (to appear)
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] The heat semigroup and kernel associated with certain non-commutative harmonic oscillators
  • Author(s): S.Taniguchi
  • Journal Title: Kyushu Jour. Math. (to appear)
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] On the Jacobi field approach to stochastic oscillatory integrals with quadratic phase functions
  • Author(s): S.Taniguchi
  • Journal Title: Kyushu Jour. of Math. (to appear)
  • Description: 「研究成果報告書概要(欧文)」より
• [Journal Article] On a class of one-dimensional Markov processes with continuous paths
  • Author(s): Nobuyuki Ikeda, Yukio Ogura
  • Journal Title: "Stochastic Analysis and Prartial Differential Equations" AMS Comtemp. Math. (To appear)
• [Book] 確率論入門I (2006)
  • Author(s): 池田信行, 小倉幸雄, 高橋陽一郎, 眞鍋昭治郎
  • Publisher: 培風館
  • Description: 「研究成果報告書概要(和文)」より