Stochastic Calculus with Infinitesimals pp 71-75

Part of the Lecture Notes in Mathematics book series (LNM, volume 2067)

Excursion to Mathematical Physics: A Radically Elementary Definition of Feynman Path Integrals

  • Frederik S. Herzberg
Chapter

Abstract

In this excursion, which is inspired by Albeverio et al. [3, Sect. 6.6] and the classical article by Nelson [58], we give another demonstration of the usefulness of radically elementary mathematics in mathematical physics, by providing a rigorous, radically elementary definition of Feynman path integrals in Minimal Internal Set Theory. A summary of these ideas—combined with a brief introduction to radically elementary mathematics for mathematical physicists and some references to previous attempts at formalizing the Feynman path integral by means of nonstandard analysis—can be found in [35].

References

  1. 3.
    Albeverio, S., Høegh-Krohn, R., Fenstad, J., Lindstrøm, T.: Nonstandard methods in stochastic analysis and mathematical physics. Pure and Applied Mathematics, vol. 122. Academic, Orlando, FL (1986)Google Scholar
  2. 35.
    Herzberg, F.: Radically elementary mathematics and the Feynman path integral. Manuscript (2012)Google Scholar
  3. 58.
    Nelson, E.: Feynman integrals and the Schrödinger equation. J. Math. Phys. 5(3), 332–343 (1964)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Frederik S. Herzberg
    • 1
    • 2
  1. 1.Institute of Mathematical EconomicsBielefeld UniversityBielefeldGermany
  2. 2.Munich Center for Mathematical PhilosophyLudwig Maximilian University of MunichMunichGermany

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