Non-differentiability of Feynman paths
Czechoslovak Mathematical Journal (2025)
- Issue: 1, page 123-139
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topMuldowney, Pat. "Non-differentiability of Feynman paths." Czechoslovak Mathematical Journal (2025): 123-139. <http://eudml.org/doc/299900>.
@article{Muldowney2025,
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.},
author = {Muldowney, Pat},
journal = {Czechoslovak Mathematical Journal},
keywords = {Feynman path integral; quantum mechanics; Brownian motion; Kurzweil-Henstock integration},
language = {eng},
number = {1},
pages = {123-139},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Non-differentiability of Feynman paths},
url = {http://eudml.org/doc/299900},
year = {2025},
}
TY - JOUR
AU - Muldowney, Pat
TI - Non-differentiability of Feynman paths
JO - Czechoslovak Mathematical Journal
PY - 2025
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
IS - 1
SP - 123
EP - 139
AB - 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.
LA - eng
KW - Feynman path integral; quantum mechanics; Brownian motion; Kurzweil-Henstock integration
UR - http://eudml.org/doc/299900
ER -
References
top- Dvoretzky, A., Erdős, P., Kakutani, S., Nonincrease everywhere of the Brownian motion process, Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probabability. Vol. 2 University of California Press, Berkeley (1961), 103-116. (1961) Zbl0111.15002MR0132608
- Feynman, R. P., Contents of Feynman's office. Group II, Section I (Correspondence), Box 26, Letter from P. Muldowney (1982), Available at https://oac.cdlib.org/findaid/ark:/13030/kt5n39p6k0/.
- Feynman, R. P., Hibbs, A. R., Quantum Mechanics and Path Integrals, International Series in Pure and Applied Physics. McGraw-Hill, New York (1965). (1965) Zbl0176.54902MR2797644
- Henstock, R., The General Theory of Integration, Oxford Mathematical Monographs. Clarendon Press, Oxford (1991). (1991) Zbl0745.26006MR1134656
- Muldowney, P., 10.1002/9781118345955, John Wiley & Sons, New York (2012). (2012) Zbl1268.60002MR3087034DOI10.1002/9781118345955
- Muldowney, P., 10.1002/9781119595540, John Wiley & Sons, Hoboken (2021). (2021) Zbl1477.60003MR4484972DOI10.1002/9781119595540
- Muldowney, P., Skvortsov, V. A., 10.1007/s11006-005-0119-7, Math. Notes 78 (2005), 228-233. (2005) Zbl1079.26007MR2245044DOI10.1007/s11006-005-0119-7
- Paley, R. E. A. C., Wiener, N., Zygmund, A., 10.1007/BF01474606, Math. Z. 37 (1933), 647-668. (1933) Zbl0007.35402MR1545426DOI10.1007/BF01474606
- Rota, G.-C., 10.1007/978-0-8176-4781-0, Modern Birkhäuser Classics. Birkhäuser, Boston (1997). (1997) Zbl1131.00005MR2374113DOI10.1007/978-0-8176-4781-0
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.