Mathematical Problems and Infinite Dimensional Analysis in Quantum Field Theory

量子场论中的数学问题和无限维分析

• 批准号: 17340032
• 负责人: ARAI Asao
• 金额: $ 6.6万
• 依托单位: Hokkaido University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17340032/
• 关键词: Hamiltonian; time operator; Heisenberg operator; quantum field; ground state; spectrum; infinite dimensional analysis; Heisenberg equation of motion; ディラック・マクスウェル作用素; 相対論的量子電磁力学; ハイゼンベルグ作用素; 生き残り確率; ポラロン; ディラック作用素; カイラル・クォーク・ソリトン; 超対称性; 基底

(1) A symmetric operator satisfying the weak Weyl relation with a Hamiltonian H (a self-adjoint operator H on a Hilbert space) is called a strong time operator of H. In this research, spectral properties of strong time operators are analyzed and important results have been obtained A. Arai, Spectrum of time operators, Lett. Math. Phys. 80 (2007), 11-17).(2) We develop a general theory of Heisenberg operators. A mathematically rigorous formulation was made on the Heisenberg equations of motion and a sufficient condition for the equation to have a unique solution was given. Moreover invariant domains are found with a discovery of new structures. This Theory is applicable not only to quantum mechanics with finite degrees of freedom, but also to quantum mechanics with infinite degrees of freedom, in particular, quantum field theory. Its range of applicability is very wide. For details, see: A. Arai, Heisenberg operators, invariant domains and Heisenberg equations of motion, Rev. Math. Phys. 19 (2007), 1045-1069.(3) Analysis was made for ground states of a quantum system interacting with a quantum field. For details, see: A. Arai, M. Hirokawa and F. Hiroshima, Regularities of ground states of quantum field models, Kyushu J. Math. 61 (2007), 321-372.

(1)一个对称算子与一个Hamilton算子H（一个Hilbert空间上的自伴算子H）满足弱Weyl关系，称为H的强时间算子。本文分析了强时间算子的谱性质，得到了一些重要结果。Arai，时间算子谱，Lett。80（2007），11-17）。(2)我们发展了海森堡算子的一般理论。对海森堡运动方程进行了严格的数学表述，给出了方程有唯一解的充分条件。此外，不变域发现了新的结构。这个理论不仅适用于有限自由度的量子力学，而且适用于无限自由度的量子力学，特别是量子场论。它的适用范围非常广泛。有关详细信息，请参见：A. Arai，Heisenberg operators，invariant domains and Heisenberg equations of motion，Rev. Math. Phys. 19（2007），1045-1069. (3)对与量子场相互作用的量子系统的基态进行了分析。有关详细信息，请参见：A. Arai，M. Hirokawa和F.广岛，量子场模型基态的规律性，九州数学杂志，61（2007），321-372。

项目成果

One-cocycles on smooth flows of weights and extended modular coactions

权重平稳流动和扩展模块化协作的单循环

• 发表时间: 2007
• 期刊: Ergodic Theory and Dynamical Systems Vol. 27
• 作者: Maria Alessandra Ragusa;Atsushi Tachikawa;Taeko Yamazaki;Michihiro Hashimoto and Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;T. Matsuyama and M. Ruzhansky;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Taeko Yamazaki;Tokio Matsuyama;Tokio Matsuyama;松山 登喜夫;Taeko Yamazaki;山崎多恵子;山崎 多恵子;Atushi Tachikawa;立川 篤;松山 登喜夫;T. YAMANOUCHI;T. YAMANOUCHI
• 通讯作者: T. YAMANOUCHI

A characterization of coactions whose fixed-point algebras contain special maximal abelian *-subalgebras

其定点代数包含特殊最大阿贝尔*-子代数的相互作用的表征

• 发表时间: 2006
• 期刊: Ergodic Theory and Dynamical Systems 26
• 作者: Y.Katayama;M.Takesaki;M.O'uchi;Y.Katayama;M.Ouchi;T.Yamanouchi;T.Yamanouchi
• 通讯作者: T.Yamanouchi

On the normalizing groupoid and the commensurability groupoids for inclusions of factors associated to ergodic equivalence rela- tions-subrelations

关于归一化群群和包含与遍历等价关系-子关系相关的因素的可通约性群群

• 发表时间: 2006
• 期刊: Journal of Functional Analysis 240
• 作者: Y.Katayama;M.Takesaki;M.O'uchi;Y.Katayama;M.Ouchi;T.Yamanouchi;T.Yamanouchi;T.Yamanouchi;A.Kishimoto;T.Yamanouchi
• 通讯作者: T.Yamanouchi

Regularities of ground states of quantum field models

量子场模型基态规律

• 发表时间: 2007
• 期刊: Kyushu Journal of Mathematics 61
• 作者: A. Arai;M. Hirokawa;F. Hiroshima
• 通讯作者: F. Hiroshima

Some aspects of representations of a quantum group in a two-dimensional system with a singular gauge potential

具有奇异规范势的二维系统中量子群表示的某些方面

• 发表时间: 2007
• 作者: A. Arai;M. Hirokawa;F. Hiroshima;Asao Arai;T.Yamanouchi;T.Yamanouchi;T.Yamanouchi;Asao Arai;Asao Arai;Asao Arai
• 通讯作者: Asao Arai