MATHEMATICAL FOUNDATIONS OF RENORMALIZATION GROUP AND THEIR APPLICATIONS TO MATHEMATICAL SCIENCES

重正化群的数学基础及其在数学科学中的应用

基本信息

  • 批准号:
    13640227
  • 负责人:
  • 金额:
    $ 1.54万
  • 依托单位:
  • 依托单位国家:
    日本
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
  • 财政年份:
    2001
  • 资助国家:
    日本
  • 起止时间:
    2001 至 2002
  • 项目状态:
    已结题

项目摘要

1. Ito and Tamura (Kanazawa Univ.) studied classical O(N) symmetric spin model by renormalization group (block spin transformation) method. In the first stage, they argued the integrability of the functional determinent det ^<-N/2>(1 + 2iGψ/√<N>) with respect to ψ, where ψ is the axially field introduced for Fourier Transformation. Using the technique called polymer (cluster) expansion, they showed that the inverse critical temperature β_c obeys the bound β_c > N log N in two dimensions, which implies the existence of strong deviation. (β_c - N for the dimension more than or equal to 3.) It is believed that β_c = ∽ in the present model.To establish this conjecture, Ito recursively applies the BST to the model to decompose the determinant into product of many determinants which comes from fluctuations of various distance scales. He showed that the main part of the recursion relations is quite simple, and reproduces the flow of the hiererchical approximation of Wilson-Dyson type.He is no … More w applying the present method (introduction of the ψ field) to the lattice gauge theory which has the same structure in principle.2. Teramoto and Ito investigated properties of turbulence, among them, the Kolmogorov law about the dissipation of energy and deviation from it. They tried to derive the deviation from the Navier-Stokes equation but they could not obtain concrete results this year.3. Shimada considered a 3D Schroedinger operator with the δ function like potential support on the sphere of the ball of radius a > 0. He discussed the convergence of the Hamiltoan as a → 0 through the resolvent convergence.4. Hiroshima investigated the Pauli-Fierz Model which is regarded as a classical Quantum Electrodynamics (QED). Hiroshima showed that the ground states of the Hamiltonian belong to the domain of the photon number operator, and also that the ground states are doubly degenerated if the spin of the electron is introduced.5. Hiroshima and Ito investigated the Pauli-Fierz Model. Though QED is believed to be trivial if no momentum cutoff is introduced, the Pauli-Fierz model may not. They apply the renormalization group type argument to the Pauli-Fierz model (this idea is originally due to J. Froelich (ETH)). But their analysis remains to be seen. Less
1.伊藤和田村(金泽大学)用重整化群(块自旋变换)方法研究了经典O(N)对称自旋模型。在第一阶段,他们论证了泛函行列式det ^&lt;-N/2&gt;(1 + 2 iG &lt;$/&lt;$)关于ψ的可积性<N>,其中ψ是为傅立叶变换引入的轴向场。利用聚合物(团簇)展开技术,他们证明了二维反临界温度β c服从β c &gt; NlogN的约束,这意味着存在很强的偏差。(当维数大于或等于3时,β_c - N。)为了证明这一猜想,Ito递归地将BST应用于该模型,将行列式分解为多个来自不同距离尺度波动的行列式的乘积。他证明了递归关系的主要部分是相当简单的,并再现了Wilson-Dyson型的层次逼近的流程。 ...更多信息 将本文的方法(引入量子场论)应用于具有相同结构的格点规范理论.寺本和伊藤研究了湍流的性质,其中,关于能量耗散和偏离的柯尔莫哥洛夫定律。他们试图从Navier-Stokes方程推导出偏离,但今年未能获得具体结果。3. Shimada考虑了一个三维Schroedinger算子,其δ函数在半径a &gt; 0的球的球面上具有类似势支集的情形。他通过预解式的收敛性讨论了当a → 0时哈密尔顿方程的收敛性.广岛研究了经典的量子电动力学(QED)Pauli-Fierz模型。广岛证明了哈密顿量的基态属于光子数算符的范围,并且证明了如果引入电子的自旋,基态会加倍简并.广岛和伊藤研究了保利-菲尔斯模型。虽然QED被认为是微不足道的,如果没有引入动量截止,保利-菲尔斯模型可能不会。他们将重整化群类型的论点应用于Pauli-Fierz模型(这个想法最初是由于J. Froelich(ETH))。但他们的分析还有待观察。少

项目成果

期刊论文数量(26)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
K.R.Ito: "Renormalization Group Recursion Formulas and Flows of Two-Dimensional O(N) Spin Model"Journal of Statistical Physics. 107. 821-856 (2002)
K.R.Ito:“二维 O(N) 自旋模型的重正化群递归公式和流程”统计物理学杂志。
  • DOI:
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    0
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F.Hiroshima: "Ground state degeneracy of the Pauli-Fierz with inlcuding spin."Adv.Theor.Math.Phys.. 5. 1091-1104 (2001)
F.Hiroshima:“包含自旋的 Pauli-Fierz 的基态简并。”Adv.Theor.Math.Phys.. 5. 1091-1104 (2001)
  • DOI:
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    0
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  • 通讯作者:
Y.Teramoto: "Global in Time Behavior of Viscous Surface Waves : Horizontally Periodic Motions"Journal of Math. Kyoto Univ.. (to appear). (2003)
Y.Teramoto:“粘性表面波的全局时间行为:水平周期性运动”数学杂志。
  • DOI:
  • 发表时间:
  • 期刊:
  • 影响因子:
    0
  • 作者:
  • 通讯作者:
K.R.Ito: "Renormalization Group Flow of Two-Dimensional O (N) Spin Model"Letters in Mathematical Physics. 58. 29-40 (2001)
K.R.Ito:《二维 O(N) 自旋模型的重正化群流》数学物理学快报。
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    0
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ITO Keiichi其他文献

Neuroscience Nursing Assessment of Facial Features Using Three-Dimensional Average Faces in Patients with Post-Acute Stroke
使用三维平均面部对急性中风后患者面部特征进行神经科学护理评估
  • DOI:
  • 发表时间:
    2013
  • 期刊:
  • 影响因子:
    0
  • 作者:
    ITO Keiichi;HARA Mikiko;YAMAUCHI Noriko;ISEKI Hiroshi
  • 通讯作者:
    ISEKI Hiroshi

ITO Keiichi的其他文献

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{{ truncateString('ITO Keiichi', 18)}}的其他基金

Applications of Renormalization Group Methods in Mathematical Sciences
重正化群方法在数学科学中的应用
  • 批准号:
    23540257
  • 财政年份:
    2011
  • 资助金额:
    $ 1.54万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Development of nobel pharmacological treatment to inhibit renal fibrosis caused by unilateral ureteral obstruction
开发抑制单侧输尿管梗阻引起的肾纤维化的诺贝尔药物治疗方法
  • 批准号:
    22590257
  • 财政年份:
    2010
  • 资助金额:
    $ 1.54万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Model Development of Palliative Management to Apply to Patients with Neurological Diseases and Families Living at Home : Three Year Follow-up
适用于神经系统疾病患者和居家家庭的姑息治疗模型开发:三年随访
  • 批准号:
    20592691
  • 财政年份:
    2008
  • 资助金额:
    $ 1.54万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Research on the practical application of detoxification of resin-based dental prosthesis by low energy electron beam irradiation
低能电子束辐照树脂基义齿脱毒实际应用研究
  • 批准号:
    20791456
  • 财政年份:
    2008
  • 资助金额:
    $ 1.54万
  • 项目类别:
    Grant-in-Aid for Young Scientists (B)
Outcome evaluation for assessing an effectiveness of home health care service for home-care neurology patients : 3 years follow-up survey
评估家庭护理神经科患者家庭保健服务有效性的结果评估:3年跟踪调查
  • 批准号:
    15592345
  • 财政年份:
    2003
  • 资助金额:
    $ 1.54万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Development of the multi-dimensional outcome scale that judges the effect of home health care service for the patients with neurological disorders and their caregivers
开发多维结果量表来判断家庭保健服务对神经系统疾病患者及其照顾者的效果
  • 批准号:
    13672485
  • 财政年份:
    2001
  • 资助金额:
    $ 1.54万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
A study of development of quality indicator that evaluates the effect of home care service for the patients with neuro-intractable diseases
神经疑难杂症患者居家护理服务效果评价质量指标的制定研究
  • 批准号:
    11672356
  • 财政年份:
    1999
  • 资助金额:
    $ 1.54万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
A study of earthquake disaster prevention system of local city in cold and snowy area of Japan, in cases of Kusiro and Hachinohe cities.
日本寒雪地区地方城市地震灾害防御体系研究——以钏路市和八户市为例
  • 批准号:
    09680451
  • 财政年份:
    1997
  • 资助金额:
    $ 1.54万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
The development of the case-mix index for screening cerebrovascular disorder's and intractable disease'spatients requiring home health nursing care
脑血管病及疑难杂症居家护理患者筛查病例组合指数的建立
  • 批准号:
    09672432
  • 财政年份:
    1997
  • 资助金额:
    $ 1.54万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
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