Stochastic Calculus with Infinitesimals

Volume 2067 of the series Lecture Notes in Mathematics pp 71-75


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

  • Frederik S. HerzbergAffiliated withInstitute of Mathematical Economics, Bielefeld UniversityMunich Center for Mathematical Philosophy, Ludwig Maximilian University of Munich

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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].