Non-differentiability of Feynman paths

被引：1

作者：

Muldowney, Pat ^{[1
]}

机构：

[1] Ulster Univ, Northland Rd, Derry BT48 7JL, North Ireland

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2025年 / 75卷 / 01期

关键词：

Feynman path integral; quantum mechanics; Brownian motion; Kurzweil-Henstock integration;

D O I：

10.21136/CMJ.2024.0493-22

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A well-known mathematical property of the particle paths of Brownian motion is that such paths are, with probability one, everywhere continuous and nowhere differentiable. R. Feynman (1965) and elsewhere asserted without proof that an analogous property holds for the sample paths (or possible paths) of a non-relativistic quantum mechanical particle to which a conservative force is applied. Using the non-absolute integration theory of Kurzweil and Henstock, this article provides an introductory proof of Feynman's assertion.

引用

页码：123 / 139

页数：17

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