On the theory of the oscillatory integral operators and its applications to the Feyman path integral for the field theory

振荡积分算子理论及其在场论费曼路径积分中的应用

• 批准号: 23540195
• 负责人: ICHINOSE Wataru
• 金额: $ 3.24万
• 依托单位: Shinshu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2013
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23540195/
• 关键词: Feyman 経路積分; Dirac 方程式; 量子電磁気学; 量子力学; Schroedinger 方程式; Feynman経路積分; Dirac方程式; Schroedinger方程式; 場の量子論; Feynmaｎ経路積分; 場の量子理論

The applicant succeeded in giving the expression of the Feynman path integral for the solutions of the Dirac equations, which describe the quantum particles in the relativistic theory. In more general, the expression of the Feynman path integral was given for the solutions of more general equations including the Dirac ones.This expression is given in the form of the "sum" of the probability amplitude satisfying the superposition principle over all possible paths that go in any direction at any speed forward and backward in time. The electrons that go backward in time are interpreted as positrons that go forward in time. This expression enables us to understand the relativistic quantum mechanics intuitively and to expect that we can construct the relativistic quantum electrodynamics in terms of a more direct method than the perturbative one used mainly in the present. The Feynman path integral for the Dirac equations has not been given for 60 years or more.

申请人成功地给出了dirac方程解的Feynman路径积分的表达，该方程描述了相对论理论中的量子粒子。在更一般而言，Feynman路径积分的表达是针对包括狄拉克（Dirac）的更通用方程的解决方案的表达，以概率幅度的“总和”的形式给出，以满足叠加原理的“总和”的形式，这些原理超过了所有速度以任何速度向前且落后的速度向前和落后。及时向后的电子被解释为及时前进的正电子。这种表达使我们能够直观地理解相对论量子力学，并希望我们可以用比现在主要使用的扰动性构建相对论量子电动力学。在60年或更长时间以来，尚未提供DIRAC方程不可或缺的Feynman Path路径。

项目成果

On the uniqueness of the polar decomposition of bounded operators in Hilbert spaces

希尔伯特空间中有界算子极分解的唯一性

• 发表时间: 2013
• 期刊: Journal of Operator Theory
• 影响因子: 0.8
• 作者: H. Takagi;H. Koshimizu and H. Ariizumi;Jun Kawabe;宇佐美広介，上村豊;Y. Taniuchi;O. Hatori;Manabu Naito;W.Ichinose and K. Iwashita
• 通讯作者: W.Ichinose and K. Iwashita

On the uniqueness of the polar decomposition of bounded operators in Hilbert space

希尔伯特空间有界算子极分解的唯一性

• 发表时间: 2013
• 期刊: Journal of Operator Theory
• 影响因子: 0.8
• 作者: W. Ichinose;K. Iwashita
• 通讯作者: K. Iwashita

Enhanced binding of the semi-relativistic Nelson model

半相对论尼尔森模型的增强绑定

• 发表时间: 2011
• 作者: Fujii;Jun Ichi;橋本隆司;M. Hirokawa and T. Kosaka;肥田野 久二男;I. Sasaki
• 通讯作者: I. Sasaki

On the Feynman path integral for nonrelativistic quantum electrodyanmics

非相对论量子电动力学的费曼路径积分

• 发表时间: 2012
• 作者: Moslehian;Mohammad Sal; Fujii;Jun Ichi;T.Nishitani;肥田野 久二男;W. Ichinose
• 通讯作者: W. Ichinose

Note on the spectrum of discrete Schroedinger operators

关于离散薛定谔算子谱的注记

• 发表时间: 2012
• 期刊: Journal of Math-for-Industry
• 作者: F. Hiroshima and I. Sasaki;T. Shirai and A. Suzuki
• 通讯作者: T. Shirai and A. Suzuki