Geometrical Properties of Feynman Path Integrals

TL;DR

This paper explores a geometric interpretation of quantum mechanics by modeling Feynman paths as geodesic trajectories of test particles in a curved space derived from the Hilbert space, providing a classical analogy.

Contribution

It introduces a novel geometric model linking Feynman paths to geodesic trajectories in a curved space within the Hilbert space framework.

Findings

Feynman paths correspond to geodesics in a curved Hilbert space

Provides a classical test particle analogy for quantum paths

Suggests a new geometric perspective on quantum mechanics

Abstract

This model is one of the possible geometrical interpretations of Quantum Mechanics where found to every image Path correspondence the geodesic trajectory of classical test particles in the random geometry of the stochastic fields background. We are finding to the imagined Feynman Path a classical model of test particles as geodesic trajectory in the curved space of Projected Hilbert space on Bloch's sphere.