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Non-perturbative analysis of quantum interaction systems

Research Project

Project/Area Number 20340032
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKyushu University

Principal Investigator

HIROSHIMA Fumio  Kyushu University, 大学院・数理学研究院, 准教授 (00330358)

Co-Investigator(Renkei-kenkyūsha) ITOU Keiichi  摂南大学, 工学部, 教授 (50268489)
HIROKAWA Masao  岡山大学, 大学院・自然科学研究科, 教授 (70282788)
MATSUI Taku  九州大学, 大学院・数理学研究院, 准教授 (50199733)
NAKANO Fumihiko  学習院大学, 理学部, 教授 (10291246)
OBATA Nobuaki  東北大学, 大学院・情報科学研究科, 教授 (10169360)
HATTORI Tetsuya  慶応大学, 経済学部, 教授 (10180902)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥11,700,000 (Direct Cost: ¥9,000,000、Indirect Cost: ¥2,700,000)
Fiscal Year 2010: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2009: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2008: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Keywords場の量子論 / 無限次元解析 / 散乱理論 / スペクトル解析 / 汎関数積分 / 基底状態 / 半群 / 確率過程 / 1パラメター半群 / レヴィー過程
Research Abstract

Ground states of quantum interaction systems are investigated. By means of functional integral representations quantum systems are studied in non-perturbative way. We show the existence and absence of ground states of the so-called Nelson model defined on a Lorentz manifold, we remove the UV cutoff by means of micro-local analysis. The asymptotic completeness of the Pauli-Fierz model defined on an indefinite Hilbert space is also established. We investigate enhanced bindings. We specify the no-binding regime of the Pauli-Fierz model and show the enhanced binding of the relativistic Nelson model. We next consider functional integrations. The heat semi-group generated by the relativistic Schroedinger operator with spin 1/2 is represented in terms of Brownian motions, Poisson processes and subordinators. By this we can derive a non-trivial energy comparison inequality. Moreover we extend this path integral representation to the Bernstein functions of the Laplacian, and apply this to a spin-boson model to show the uniqueness of the ground state. We furthermore succeeded to construct an infinite volume limit of the Gibbs measure with double stochastic integral as potential.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (61 results)

All 2011 2010 2009 2008 Other

All Journal Article (27 results) (of which Peer Reviewed: 20 results) Presentation (30 results) Book (4 results)

  • [Journal Article] Infrared problem for the Nelson model with variable coefficients, to appear in Commun.2011

    • Author(s)
      C.Gerard, F.Hiroshima, A.Panati, A.Suzuki
    • Journal Title

      Math.Phys.

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Infrared problem for the Nelson model with variable coefficients2011

    • Author(s)
      C.Gerard, F.Hiroshima, A.Panati, A.Suzuki
    • Journal Title

      Communications in Mathematical Physics

      Volume: (印刷中)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the ionization energy of semi-relativistic Pauli-Fierz model for a single particle2010

    • Author(s)
      F.Hirosihma, I.Sasaki
    • Journal Title

      RIMS Kokyuroku Bessatsu B21

      Pages: 25-34

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence and absence of ground states for a particle interacting through the quantized scalar field on a static spacetime2010

    • Author(s)
      C.Gerard, F.Hiroshima, A.Panati, A.Suzuki
    • Journal Title

      RIMS Kokyuroku Bessatsu B21

      Pages: 15-24

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Pauli-Fierz model with Kato-class potentials and exponential decays2010

    • Author(s)
      T.Hidaka, F.Hiroshima
    • Journal Title

      Rev.Math.Phys. 22

      Pages: 1181-1208

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence and absence of ground states for a particle interacting through the quantized scalar field on a static spacetime2010

    • Author(s)
      C.Gerard, F.Hiroshima, A.Panati, A.Suzuki
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: 21 Pages: 15-24

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pauli-Fierz model with Kato-class potentials and exponential decays2010

    • Author(s)
      T.Hidaka, F.Hiroshima
    • Journal Title

      Reviews in Mathematical Physics

      Volume: 22 Pages: 1181-1208

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Feynman-Kac type formula for Schrodinger semigroup with Bernstein function of Laplacian2010

    • Author(s)
      F.Hiroshima
    • Journal Title

      京大数理研講究録

      Volume: 1696 Pages: 119-143

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Physical state of nonrelativistic quantum electroduynamics2009

    • Author(s)
      F.Hiroshima, A.Suzuki
    • Journal Title

      Ann.Henri Poincare 10

      Pages: 913-953

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Infrared divergence of a scalar quantum field model on a pseudo Riemannian manifold2009

    • Author(s)
      C.Gerard, F.Hiroshima, A.Panati, A.Suzuki
    • Journal Title

      Interdisciplinary Information Science 15

      Pages: 399-422

    • NAID

      130000120888

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Gibbs measures with double stochastic integrals on path space, Infinite Dimensional Analysis2009

    • Author(s)
      V.Betz, F.Hiroshima
    • Journal Title

      Quantum Probability and Related Topics 12

      Pages: 135-152

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Physical state of nonrelativistic quantum electrodynamics2009

    • Author(s)
      F.Hiroshima, A.Suzuki
    • Journal Title

      Ann. Henri Poincare 10

      Pages: 913-153

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Infrared divergence of a scalar quantum field model on a pseudo Riemannian manifold2009

    • Author(s)
      C.Gerard, F.Hiroshima, A.Panatti, A.Suzuki
    • Journal Title

      Interdisciplinary Information Science 15

      Pages: 399-422

    • NAID

      130000120888

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Gibbs measures with double stochastic integrals on path space2009

    • Author(s)
      V.Betz, F.Hiroshima
    • Journal Title

      Infinite Dimensional Analysis, Quantum Probability and Related Tonics 12

      Pages: 135-152

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Path integrations of relativistic Schroediriger operators and Bernstein functions2009

    • Author(s)
      廣島文生
    • Journal Title

      京大数理研講究録 1658

      Pages: 18-34

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Strong time operator associated with generalized Hamiltonians2009

    • Author(s)
      F. Hiroshima, S. Kuribayashi, Y. Matsuzawa
    • Journal Title

      Lett. Math. Phys. 87

      Pages: 115-123

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Gibbs measure with double stochastic integrals on path space2009

    • Author(s)
      V. Betz, F. Hiroshima
    • Journal Title

      Inf. Dim. Anal. and Quant. Prob. (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Perturbation of embedded eigenvalues in quantum field theory2008

    • Author(s)
      F.Hiroshima
    • Journal Title

      Sugaku exposition 21

      Pages: 177-207

    • Related Report
      2010 Final Research Report
  • [Journal Article] Enhanced binding of an N particle system interacting with a scalar field I2008

    • Author(s)
      F.Hiroshima, I.Sasaki
    • Journal Title

      Math.Z. 259

      Pages: 657-680

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Functional integral representations of the Pauli-Fierz model with spin 1/22008

    • Author(s)
      F.Hiroshima, J.Lorinczi
    • Journal Title

      J.Funct.Anal. 254

      Pages: 2127-2185

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Functional integral representation of the Pauli-Fierz modelwith spin 1/22008

    • Author(s)
      F. Hiroshima, J. Lorinczi
    • Journal Title

      J. Funct. Anal. 254

      Pages: 2127-2185

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Enhanced binding of an N particle system interactingwith a scalar field I2008

    • Author(s)
      F. Hiroshima, I. Sasaki
    • Journal Title

      Math. Z 259

      Pages: 657-680

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Perturbation of embedded eigenvalues in quantum field theory2008

    • Author(s)
      F. Hiroshima
    • Journal Title

      Sugaku exposition 21

      Pages: 177-207

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Functional integral representations of nonrelativistic QED2008

    • Author(s)
      F. Hiroshima
    • Journal Title

      京大数理研講究録 1600

      Pages: 68-91

    • Related Report
      2008 Annual Research Report
  • [Journal Article] N体スカラー場のenhanced binding2008

    • Author(s)
      F. Hiroshima, I. Sasaki
    • Journal Title

      京大数理研講究録 1609

      Pages: 120-131

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Self-adjoint extensions of momentum operators : application of weak Weylrelations

    • Author(s)
      F.Hiroshima, S.Kuribayashi, I.Sasaki
    • Journal Title

      J. Math-for-Industry (印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Feynman-Kac formula Schroedinger semigroup with Bernstein function of the Laplacian

    • Author(s)
      廣島文生
    • Journal Title

      京大数理研講究録 (印刷中)

    • Related Report
      2009 Annual Research Report
  • [Presentation] Feynman-Kac type formula with cadlag path and generalized Schro\" odinger operator with spin2010

    • Author(s)
      F.Hiroshima
    • Organizer
      基研研究会
    • Place of Presentation
      京大基礎物理学研究所
    • Year and Date
      2010-11-06
    • Related Report
      2010 Final Research Report
  • [Presentation] Feynman-Kac type formula with cadlag path and generalized Schrodinger operator with spin2010

    • Author(s)
      廣島文生
    • Organizer
      基研研究会
    • Place of Presentation
      京大基礎物理学研究所
    • Year and Date
      2010-11-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] Spectral analysis of QFT by functional integration with jump processes2010

    • Author(s)
      F.Hiroshima
    • Organizer
      Stochastic Process and their Applications 2010
    • Place of Presentation
      大阪
    • Year and Date
      2010-09-10
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Relativistic Feynmann-Kac formula and its applications2010

    • Author(s)
      F.Hiroshima
    • Organizer
      第122回日本数学会九州支部例会
    • Place of Presentation
      九大西新プラザ
    • Year and Date
      2010-02-13
    • Related Report
      2010 Final Research Report
  • [Presentation] Feshbach mapとBirman-Schwinger原理によるQEDのenahanced binding2010

    • Author(s)
      F.Hiroshima
    • Organizer
      作用素論研究集会
    • Place of Presentation
      松本中央公民館
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Spectral analysis pf relativistic PF model in QED2009

    • Author(s)
      廣島文生
    • Organizer
      スペクトル散乱理論とその周辺
    • Place of Presentation
      京大
    • Year and Date
      2009-12-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] Relativistic PF model in QED by path measures2009

    • Author(s)
      廣島文生
    • Organizer
      数学的場の量子論とくりこみ理論
    • Place of Presentation
      西新プラザ(福岡)
    • Year and Date
      2009-11-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] Relativistic QFT by path measures2009

    • Author(s)
      F.Hiroshima
    • Organizer
      九州確率論研究会
    • Place of Presentation
      九大西新プラザ
    • Year and Date
      2009-11-14
    • Related Report
      2010 Final Research Report
  • [Presentation] Spectral analysis of Schroedinger operators by path measures II2009

    • Author(s)
      廣島文生
    • Organizer
      確率論とその周辺
    • Place of Presentation
      東北大学
    • Year and Date
      2009-11-05
    • Related Report
      2009 Annual Research Report
  • [Presentation] Spectral analysis of Schroedinger operators by path measures I2009

    • Author(s)
      廣島文生
    • Organizer
      確率論とその周辺
    • Place of Presentation
      東北大学
    • Year and Date
      2009-11-04
    • Related Report
      2009 Annual Research Report
  • [Presentation] Bernstein関数のLapalcianを持ったSchrodinger作用素の経路積分2009

    • Author(s)
      F.Hiroshima
    • Organizer
      日本数学会
    • Place of Presentation
      阪大
    • Year and Date
      2009-09-24
    • Related Report
      2010 Final Research Report
  • [Presentation] Relativistic Feynman-Kac formula with spin through Levy process2009

    • Author(s)
      廣島文生
    • Organizer
      第11回広島応用解析セミナー
    • Place of Presentation
      広島大学
    • Year and Date
      2009-09-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] 非相対論的量子電気力学における物理的空間の非自明性2009

    • Author(s)
      A.Suzuki
    • Organizer
      日本数学会
    • Place of Presentation
      東大
    • Year and Date
      2009-03-26
    • Related Report
      2010 Final Research Report
  • [Presentation] Spectral analysis of relativistic Pauli-Fierz model in QED2009

    • Author(s)
      F.Hiroshima
    • Organizer
      RIMS研究会スペクトル・散乱理論とその周辺
    • Place of Presentation
      京大
    • Related Report
      2010 Final Research Report
  • [Presentation] Relativistic Pauli-Fierz model in QED by path measures2009

    • Author(s)
      F.Hiroshima
    • Organizer
      数学的場の量子論とくりこみ理論
    • Place of Presentation
      九大西新プラザ
    • Related Report
      2010 Final Research Report
  • [Presentation] Spectral analysis of relativistic Schrodinger operators by path measures II2009

    • Author(s)
      F.Hiroshima
    • Organizer
      確率解析とその周辺
    • Place of Presentation
      東北大
    • Related Report
      2010 Final Research Report
  • [Presentation] Spectral analysis of relativistic Schrodinger operators by path measures I2009

    • Author(s)
      F.Hiroshima
    • Organizer
      確率解析とその周辺
    • Place of Presentation
      東北大
    • Related Report
      2010 Final Research Report
  • [Presentation] Relativistic Feynman-Kac formula with spin through Levy process2009

    • Author(s)
      F.Hiroshima
    • Organizer
      第11回広島応用解析セミナー
    • Place of Presentation
      広大
    • Related Report
      2010 Final Research Report
  • [Presentation] Path Integral and Field Theory Model2009

    • Author(s)
      F.Hiroshima
    • Organizer
      数理物理学若手セミナー
    • Place of Presentation
      摂南大
    • Related Report
      2010 Final Research Report
  • [Presentation] Spectral analysis by path measures in QFT2008

    • Author(s)
      F. Hiroshima
    • Organizer
      The 8^<th> Sendai workshop on infinite dimensionalanalysis and quantum probability
    • Place of Presentation
      東北大学
    • Year and Date
      2008-11-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] Semi-relativistic Pauli-Fierz modelby path measures2008

    • Author(s)
      F. Hiroshima
    • Organizer
      非可換ミクロ・マクロ双対性
    • Place of Presentation
      京大数理研
    • Year and Date
      2008-11-04
    • Related Report
      2008 Annual Research Report
  • [Presentation] Quantum field theory by path mesures2008

    • Author(s)
      F. Hiroshima
    • Organizer
      Paris XI University 談話会
    • Place of Presentation
      Paris XI 大学(フランス)
    • Year and Date
      2008-10-29
    • Related Report
      2008 Annual Research Report
  • [Presentation] Analysis of ground states in QFT by functional integration2008

    • Author(s)
      F. Hiroshima
    • Organizer
      The 24^<th> Max Born symposium
    • Place of Presentation
      Wroclaw大学(ポーランド)
    • Year and Date
      2008-09-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] Analysis of ground states by Gibbs measures2008

    • Author(s)
      F. Hiroshima
    • Organizer
      Loughborough University 談話会
    • Place of Presentation
      Loughborough大学(英国)
    • Year and Date
      2008-09-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] Spectral analysis of QFT model by functional integrations2008

    • Author(s)
      F. Hiroshima
    • Organizer
      第5回日独シンポジウム
    • Place of Presentation
      西新プラザ(福岡)
    • Year and Date
      2008-09-08
    • Related Report
      2008 Annual Research Report
  • [Presentation] 量子場のハミルトニアンの基底状態の存在と非存在について・廣島の方法による深化発展2008

    • Author(s)
      F.Hiroshima
    • Organizer
      場の理論に動機づけを持つ数学の諸問題
    • Place of Presentation
      佐賀大
    • Related Report
      2010 Final Research Report
  • [Presentation] Spectral analysis by path measures in QFT2008

    • Author(s)
      F.Hiroshima
    • Organizer
      8th Sendai Workshop on Infinite Dimensional Analysis and Quantum Probability
    • Place of Presentation
      東北大
    • Related Report
      2010 Final Research Report
  • [Presentation] Semi-relativistic Pauli-Fierz model by path mesures2008

    • Author(s)
      F.Hiroshima
    • Organizer
      RIMS研究会,非可換解析とミクロ・マクロ双対性
    • Place of Presentation
      京大
    • Related Report
      2010 Final Research Report
  • [Presentation] Spectral analysis of QFT by functional integrations, Stochastic analysis and applications2008

    • Author(s)
      F.Hiroshima
    • Organizer
      日独シンポ
    • Place of Presentation
      九大西新プラザ
    • Related Report
      2010 Final Research Report
  • [Presentation] Analysis of ground states in quantum field theory by functional integrations2008

    • Author(s)
      F.Hiroshima
    • Organizer
      The 24th Max Born Symposium
    • Place of Presentation
      Wroclaw大学・ポーランド
    • Related Report
      2010 Final Research Report
  • [Book] Feynman-Kac-Type Theorems and Gibbs Measures on Path Space(With Applications into Rigorous Quantum Field Theory, Walter de Gruyter)2011

    • Author(s)
      V.Betz, F.Hiroshima, J.Lorinczi
    • Total Pages
      503
    • Publisher
      Studies in Mathematics 34
    • Related Report
      2010 Final Research Report
  • [Book] Feynman-Kac-Type Theorems and Gibbs Measures on Path Space.with Applications into Rigorous Quantum Field Theory2011

    • Author(s)
      V.Betz, F.Hiroshima, J.Lorinczi
    • Total Pages
      503
    • Publisher
      Walter de Gruyter, Studies in Mathematics 34(5月出版予定)
    • Related Report
      2010 Annual Research Report
  • [Book] 確率論的場の理論(「数理科学」)2008

    • Author(s)
      廣島文生
    • Total Pages
      8
    • Publisher
      サイエンス社
    • Related Report
      2010 Final Research Report
  • [Book] 数理科学12月号・特集確率論的物理観2008

    • Author(s)
      廣島 文生, その他
    • Total Pages
      100
    • Publisher
      サイエンス社
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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