Czechoslovak Mathematical Journal, first online, pp. 1-17
Non-differentiability of Feynman paths
Pat Muldowney
Received October 23, 2022. Published online March 8, 2024.
Abstract: 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.
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