Research on Operator Analysis for Nonrelativistic Quantum Dynamics in High Energy Region

高能区非相对论量子动力学算子分析研究

• 批准号: 16540155
• 负责人: HIROKAWA Masao
• 金额: $ 2.37万
• 依托单位: OKAYAMA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540155/
• 关键词: Nonrelativistic QED; Operator Analysis; Ultraviolet Cutoff

There are some mathematical problems in nonrelativistic quantum electrodynamics. Especially, we have been concerned with ultraviolet catastrophe in high energy region and moreover infrared catastrophe after removing ultraviolet cutoff.Hirokawa established some problems on ultraviolet catastrophe and/or infrared castastrophe in mathematics. Hiroshima and Spohn investigated the renormalized mass of electron. Hirokawa, Hiroshima, and Spohn have succeeded in removing both, ultraviolet and infrared cutoffs for the so-called Nelson model, which describes the electron coupled with photons in such as hydrogen-like atom. Also, Hirokawa clarified that the result by the regular perturbation theory is still available in the above model after removing both cutoffs in collaboration with Hainzl and Spohn. They employed a nonperturbative method to prove it.Hirokawa studied scattering theory with Tamura, problem on singularity of ultraviolet catastrophe with Tanaka, and uniqueness of the ground state with Sato.

在非同性量子电动力学中存在一些数学问题。尤其是，我们一直关注高能区域的紫外线灾难，此外，除了紫外线截止后，红外灾难。Hirokawa在数学中在紫外线灾难和/或红外红外冠状动脉粥样硬化上确定了一些问题。广岛和Spohn研究了重新归一化的电子质量。 Hirokawa，Hiroshima和Spohn成功地为所谓的Nelson模型删除了紫外线和红外临界值，该模型描述了类似氢原子的电子和光子的电子。此外，Hirokawa澄清说，在与Hainzl和Spohn合作删除两个截止后，常规扰动理论的结果仍然可以在上述模型中获得。他们采用了一种非扰动方法来证明这一点。Hirokawa用塔穆拉（Tamura）研究了散射理论，塔纳卡（Tanaka）紫外线灾难的奇异性问题以及佐藤（Sato）的基础状态的独特性。

项目成果

Solvability of the functional equation f=(T-I)h for vector-valued functions

向量值函数的函数方程 f=(T-I)h 的可解性

• 发表时间: 2004
• 期刊: Colloq.Math. 99
• 作者: 高橋泰嗣;高橋泰嗣;Tomonari Suzuki;Yasuji Takahashi;Yasuji Takahashi;Tomonari Suzuki;Yasutaka Yamada;加藤幹雄;Jyunji Inoue;Lasha Ephremidze;Hiroyuki Takagi;Hiroyuki Takagi;山田康隆;高木康啓行;Sin-Ei Takahasi;山田康隆;田村高幸;田村高幸;高橋泰嗣;Takeshi Miura;Yasutaka Yamada;Makoto Tsukada;Yasutaka Yamada;Hiroyuki Takagi;Yasutaka Yamada;Takayuki Tamura;Takayuki Tamura;Yasuji Takahashi;Takeshi Miura;Makoto Tsukada;山田康隆;Takeshi Miura;山田康隆;山田康隆;高橋泰嗣;Yasutaka Yamada;山田康隆;高橋泰嗣;Ryotaro Sato;Sin-Ei Takahasi;Mikio Kato;Yasuji Takahashi;Yasutaka Yamada;Yasuji Takahashi;Yasutaka Yamada;Sin-Ei Takahashi;Ryotaro Sato
• 通讯作者: Ryotaro Sato

Scattering of Dirac particles by electromagnetic fields with small support in two dimensions and effect from scalar potentials

二维小支撑电磁场对狄拉克粒子的散射以及标量势的影响

• 发表时间: 2004
• 期刊: Annales Henri Poincare 5・1
• 作者: Hiroshi T.ITO;Osanobu YAMADA;Chiaki TSUKAMOTO;Shin-ich DOI;Shin-ichi DOT;Hideo TAMURA
• 通讯作者: Hideo TAMURA

On the range of a closed operator in an $Lsb 1$-space of vector-valued functions

关于向量值函数的 $Lsb 1$ 空间中闭运算符的范围

• 发表时间: 2005
• 期刊: Comment. Math. Univ. Carolin. 46
• 作者: 内藤 敏機;申 正善;M.Hirokawa;C.Hainzl;R.Sato
• 通讯作者: R.Sato

Ground state for point particles interacting through a massless scalar Bose field

通过无质量标量玻色场相互作用的点粒子的基态

• 发表时间: 2005
• 期刊: Adv.Math. 191
• 作者: T.Ichinose;H.Tamura;廣川 真男(他2名)
• 通讯作者: 廣川 真男(他2名)

A model of interband radiative transition

带间辐射跃迁模型

• 发表时间: 2004
• 期刊: Journal of Mathematical Soiety of Japan 56
• 作者: J.Dittrich;P.Exner;M.Hirokawa
• 通讯作者: M.Hirokawa