Interpretation of Feynman formalism of quantum mechanics in terms of probabilities of paths

TL;DR

This paper revisits Feynman path integrals in quantum mechanics, compares them with classical wave and diffusion models, and proposes a probabilistic reformulation that derives scattering results without relying on the traditional Born rule.

Contribution

It introduces a reformulation of Feynman path integrals where transition probabilities are summed over paths, providing a particle-based interpretation without assuming wavefunction probability density.

Findings

Derived the Born approximation within the new formalism

Proposed a probabilistic interpretation of path integrals

Compared quantum paths with classical wave and Brownian motion

Abstract

Feynman path integrals formalism for non-relativistic quantum mechanics is revisited. A comparison is made with the cases of light progagation (Huygens principle) and Brownian motion. The difficulties for a physical model behind Feynman formalism are pointed out. It is proposed a reformulation where the transition probability from one space-time point to another one is the sum of probabilities of the possible paths. The Born approximation for scattering is derived within the formalism, which suggests an interpretation in terms of particles, without the need of Born assumption that the modulus squared of the wavefunction is a probability density.