Non-differentiability of Feynman paths

被引：0
|
作者：
Muldowney, Pat [1 ]
机构：
[1] Ulster Univ, Northland Rd, Derry BT48 7JL, North Ireland
来源：
CZECHOSLOVAK MATHEMATICAL JOURNAL | 2024年 / 75卷 / 1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
收藏
页码：123 / 139
页数：17
相关论文
共 50 条
  • [21] Order Disorder Transition in Nanostructures via Non-Differentiability
    Casian-Botez, I.
    Agop, M.
    JOURNAL OF COMPUTATIONAL AND THEORETICAL NANOSCIENCE, 2015, 12 (08) : 1746 - 1755
  • [22] First-order risk aversion and non-differentiability
    Uzi Segal
    Avia Spivak
    Economic Theory, 1997, 9 : 179 - 183
  • [23] Cone unrectifiable sets and non-differentiability of Lipschitz functions
    Maleva, Olga
    Preiss, David
    ISRAEL JOURNAL OF MATHEMATICS, 2019, 232 (01) : 75 - 108
  • [24] The moduli of non-differentiability for Gaussian random fields with stationary increments
    Wang, Wensheng
    Su, Zhonggen
    Xiao, Yimin
    BERNOULLI, 2020, 26 (02) : 1410 - 1430
  • [25] Non-differentiability Sets for Cantor Functions with respect to Various Expansions
    Ikeda, K.
    AZERBAIJAN JOURNAL OF MATHEMATICS, 2016, 6 (01): : 52 - 78
  • [26] Non-differentiability of payoff functions and non-uniqueness of nash equilibria
    Wageningen Universiteit, Sociale Wetenschappen, Hollandseweg 1, 6700 EW Wageningen, Netherlands
    Int. J. Comput. Math. Sci., 2009, 8 (391-396):
  • [27] FLOW DYNAMICS REGIMES VIA NON-DIFFERENTIABILITY IN COMPLEX FLUIDS
    Axinte, Ciprian Iulian
    Baciu, Constantin
    Volovat, Simona
    Tesloianu, Dan
    Borsos, Zoltan
    Baciu, Anca
    Agop, Maricel
    UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2014, 76 (02): : 233 - 242
  • [28] HYSTERETIC TYPE BEHAVIORS OF THE COMPLEX FLUIDS VIA NON-DIFFERENTIABILITY
    Timofte, Daniel
    Ochiuz, Lacramioara
    Eva, Lucian
    Moraru, Evelina
    Stana, Bogdan
    Agop, Maricel
    Vasincu, Decebal
    PROCEEDINGS OF THE ROMANIAN ACADEMY SERIES A-MATHEMATICS PHYSICS TECHNICAL SCIENCES INFORMATION SCIENCE, 2014, 15 (04): : 331 - 337
  • [29] SETS OF NON-DIFFERENTIABILITY FOR FUNCTIONS WITH FINITE LOWER SCALED OSCILLATION
    Hanson, Bruce H.
    REAL ANALYSIS EXCHANGE, 2016, 41 (01) : 87 - 100
  • [30] A non-differentiability result for the inversion operator between Sobolev spaces
    Farkas, G
    Garay, BM
    ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2000, 19 (03): : 639 - 654
12345