A New Derivation of the Propagator's Path Integral for Spinless Elementary Particles

TL;DR

This paper presents a novel derivation of the propagator's path integral for spinless particles using a primitive ontology and indistinguishability of paths, connecting classical and quantum descriptions under certain conditions.

Contribution

It introduces a new framework based on isolated units and path indistinguishability, deriving quantum motion from classical-like assumptions for spinless particles.

Findings

Derivation of quantum propagator from classical assumptions

Framework applicable in weak fields and low velocities

Potential implications for weak relativistic effects

Abstract

We introduce a notion of isolated units, elementary particles or more general physical phenomena that do not significantly affect their surrounding environment, and we build a primitive ontology to describe their evolution and interaction. We further introduce a notion of indistinguishability of distinct spacetime paths of a unit, for which the evolution of the state variables of the unit is the same, and a generalization of the equivalence principle based on indistinguishability. Under a time invertibility condition on the whole set of indistinguishable paths of a unit, we show that the quantization of motion of spinless elementary particles in a general potential field can be derived in this framework, in the limiting case of weak fields and low velocities. Extrapolating this approach to include weak relativistic effects, we explore possible experimental consequences.