Feynman path integral using Lebesgue-Bochner-Stieltjes integration

It was known as Feynman Path Integrals in quantum physics, and a large part of the scientific community still considers them as a heuristic tool that lacks sound mathematical definition. This paper aims to refute this prejudice by providing an extensive and self-contained description of the mathematical theory of Feynman Path Integration, from the earlier attempts to the lates

According to de Brogli, it was realized that light could in fact show behavioral characteristics of both waves and particles. It was demonstrated that electrons show the same dual behavior of matter which was later extended to atoms and molecules. We shall follow the method of integration by the generalized Bochner-Lebesgue-Steilltjes method of integration in Banach space. We demonstrate that the Feynman Path Integral is consistent and can be justified mathematically with the Bogdan integration approach.