Mathematical Analysis of a System of a Dirac Particle Interacting With a Quantum Electronagnetid Field

狄拉克粒子与量子电磁场相互作用系统的数学分析

• 批准号: 13440039
• 负责人: ARAI Asao
• 金额: $ 3.46万
• 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: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-13440039/
• 关键词: Dirac particle; Dirac operator; Dirac-Maxwell operator; Fock space; Scaling limit; Enhanced binding; 基底状態; 非相対論的QED; 量子場; パウリーフィールツモデル; エンハンストバインディング; 量子電磁場; 量子電磁力学

(i)A Hamiltonian H of a quantum system of a Dirac particle interacting with a quantum electromagnetic field is described by a Dirac-Maxwell operator. The nonrelativistic limit of H is considered. It is proven that a scaled Hamiltonian H_c with a parameter c converges in the strong resolvent sense to the Pauli-Fierz Hamiltonian as c tends to infinity.(ii)Existence of a scaling limit of H which yields an effective Hamiltonian of the quantum system under consideration.(iii)Existence of the enhanced binding of a class of quantum systems in nonrelativisitc quantum field theory.

(i)A狄拉克粒子与量子电磁场相互作用的量子系统的汉密尔顿量H由狄拉克-麦克斯韦算符描述。考虑了H的非相对论极限。证明了当c趋于无穷大时，带参数c的标度哈密顿量H_c在强预解式意义下收敛于Pauli-Fierz哈密顿量.（ii）H的标度极限的存在，它产生了所考虑的量子系统的有效哈密顿量。（iii）非相对论量子场论中一类量子系统增强束缚的存在性。

项目成果

Asao Arai: "Enhanced binding in a general class of quantum field models"Rev.Math.Phys.. 15. 387-423 (2003)

Asao Arai：“增强了一般类量子场模型中的结合”Rev.Math.Phys.. 15. 387-423 (2003)

Asao Arai: "Enhanced binding in models of nonrelativistic quantum field theory"A Garden of Quanta (World Scientific). 197-207 (2003)

Asao Arai：“非相对论量子场论模型中的增强结合”量子花园（世界科学）。

Asao Arai: "Ground state of the massless Nelson model without infrared cutoff in a non-Fock representation"Rev.Math.Phys.. 13. 1075-1094 (2001)

Asao Arai：“非福克表示中无红外截止的无质量尼尔森模型的基态”Rev.Math.Phys.. 13. 1075-1094 (2001)

Asao Arai: "Non-relativistic limit of a Dirac-Maxwell operator in relativistic quantum electrodynamics"Reviews in Mathematical Physics. 15. 245-270 (2003)

Asao Arai：“相对论量子电动力学中狄拉克-麦克斯韦算子的非相对论极限”数学物理学评论。

Asao arai: "Mathematical Theory of Quantum Particles Interacting With a Quantum Field"Quantum Probability and White Noise Analysis. 16. 1-48 (2003)

Asao arai：“量子粒子与量子场相互作用的数学理论”量子概率和白噪声分析。