Application of the pseudo-differential operotous to the Feynmon path

伪微分运算在Feynmon路径中的应用

基本信息

批准号：
10640176
负责人：
ICHINOSE Wataru
金额：
$ 1.86万
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：
1998
资助国家：
日本
起止时间：
1998 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640176/
关键词：
pendo-diffenntial fouri intogral oporotoo Schrodinsyr eguotion path integral Feynman

项目摘要

The aim of our project was to give the rigorous meaning to the Feynman path integrals used in physics. In detail, we study : (1) We give the rigorous meaning to the Feynman path integrals in phase space.(2) We give the rigorous meaning to the path integral representations of correlation functions and generating functions Z (J) in quantum mechanics and also quantum free field. Doc.N.Kumano-go was made responsible for a part of the study of the path integral by means of Fourier integral operators.We can say about our reserch result that our aim was completed except for the study of quntum free field as will be stated. In the paper [1] we proved convergence of the Feynman path integral in confuguration space independently of the choice of electromagnetic potentials, which implies the gauge invariance of the Feynman path integrals and generalizes the results proved in the author's paper in C.M.P (1997). From this result we can get the path integral representation of Z (J) in quantumm mechanics. In [2] we modified the definition of the path integral in phase space used in physics and showed its gauge invariance, convergence and the fact that this path integral in phase space is equal to the path integral in confuguration space familiar in physics. In [3] we gave the rigorous meaning to the path integral representation of correlation functions including not only position operators but also momentum operators. Here the path integrals in phase space in [2] was essentially used. In [4,5] Kumano-go gave a simple proof of convergence of the kernel of the path integral defined through piecewise classical paths by using the Fourier integral operators. In [6], usnig the same method, Kumano-go gave a simple proof of the path integral defined through broken line paths.

我们项目的目的是将严格的含义赋予物理中使用的Feynman路径积分。详细研究我们研究：（1）我们在相空间中的Feynman路径积分中给出了严格的含义。（2）我们为相关函数的路径积分表示的严格含义赋予了量子力学和量子无量子场的函数z（j）。 doc.n.kumano-go通过傅立叶积分运算符对路径积分不可或缺的一部分负责。我们可以说，我们的回归结果是，除了对Quntum自由领域的研究外，我们的目标已完成。在论文[1]中，我们证明了Feynman Path在混淆空间中积分的收敛性，独立于选择电磁电位，这意味着Feynman Path积分的规格不变性，并概括了C.M.P（1997）在作者论文中证明的结果（1997年）。从此结果，我们可以在Quantumm力学中获得Z（J）的路径积分表示。在[2]中，我们修改了物理中使用的相空间中的路径积分的定义，并显示了其规格不变性，收敛性以及相位空间中的该路径积分等于物理中熟悉的混淆空间中的路径积分。在[3]中，我们给了相关函数的路径积分表示的严格含义，不仅包括位置操作员，而且还包括动量运算符。在这里，基本上使用了[2]中相空间中的路径积分。在[4,5]中，kumano-go通过使用傅立叶积分运算符，简单地证明了通过分段经典路径定义的路径积分内核的简单证明。在[6]中，USNIG相同的方法，Kumano-go简单地证明了通过破裂的线路路径定义的路径积分。