Spectral analysis of quantum field theory by means of functional integrations

通过泛函积分对量子场论进行谱分析

• 批准号: 22654018
• 负责人: HIROSHIMA Fumio
• 金额: $ 1.24万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2010
• 资助国家: 日本
• 起止时间: 2010 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22654018/
• 关键词: 関数解析; 場の量子論; 無限次元解析; スペクトル散乱理論; スペクトル解析; 汎関数積分; 基底状態; レヴィー過程; シュレディンガー作用素; 散乱理論; 半群; 確率過程

According to purpose(I),(II) and(III) proposed in KENKYU-KEIKAKU-CHOSHO, we review results obtained by Grant-in-Aid for Challenging Exploratory Research.(I) The functional integral representation of the heat semi-group generated by the relativistic PF model is constructed in terms of three stochastic processes, Euclidean field, Brownian motion and subordinator. By using this we show the essential self-adjointness of PF model, decay of bound states and the uniqueness of ground state.(II) Enhanced binding of the many-body relativistic Nelson model is shown with Itaru Ssasaki(Shinshu university). A functional integral representation is a key ingredient. The result was sent to an international journal for publication.(III) The Nelson model defined on a pseudo Riemannian manifold is studied with C. Gerard(Paris XI), Akito Suzuki(Shinshu university) and Annalisa Panati(Toulon-Var). We published papers in international journals.

根据KENKYU-KEIKAKU-CHOSHO中提出的目的(I)、(II)和(III)，我们回顾了Grant-in-Aid for Challengative探索性研究的结果：(I)根据欧几里德场、布朗运动和从属三个随机过程，构造了由相对论PF模型生成的热半群的泛函积分表示。由此我们证明了PF模型的本质自伴性、束缚态的衰变和基态的唯一性。(Ii)用新树大学的Itaru Ssasaki证明了多体相对论Nelson模型的增强束缚。泛函积分表示是一个关键因素。(Iii)与C.Gerard(Paris XI)、Akito Suzuki(Shinshu University)和Annalisa Panati(Toulon-Var)共同研究了伪黎曼流形上的Nelson模型。我们在国际期刊上发表了论文。

项目成果

Infrared problem for the Nelson model with variable coefficients

变系数 Nelson 模型的红外问题

• 期刊: Communucations in Mathematical Physics
• 作者: C.Gerard;F.Hiroshima;A.Pnati;A.Suzuki
• 通讯作者: A.Suzuki

The Nelson model on a static Lorentzian manifold

静态洛伦兹流形上的尼尔森模型

• 发表时间: 2012
• 期刊: RIMS
• 作者: Yuhei Yamamoto;Tomoaki Togashi and Kiyoshi Kat.;F. Hiroshima
• 通讯作者: F. Hiroshima

Spectral analysis of QFT by functional integration with jump processes

通过与跳跃过程的功能集成进行 QFT 谱分析

• 发表时间: 2010
• 作者: Takuma Matsumoto;Kiyoshi Kato;Masanobu Yahiro;F. Hiroshima
• 通讯作者: F. Hiroshima

Infrared problem for the Nelson model with variable coefficients Commun. Math. Phys.

具有可变系数 Commun 的 Nelson 模型的红外问题。

• 发表时间: 2011
• 作者: C. Gerard;F. Hiroshima;A. Panati and A. Suzuki
• 通讯作者: A. Panati and A. Suzuki

Relativistic Pauli-Fierz model

相对论泡利-菲尔兹模型

• 发表时间: 2011
• 期刊: COE Lecture Note
• 作者: Kiyoshi Kato;Yuhei Yamamoto;Tomoaki Togashi;F. Hiroshima
• 通讯作者: F. Hiroshima