A physical basis for the phase in Feynman path integration

TL;DR

This paper proposes that the phase in Feynman path integrals has a physical origin related to time reversal, suggesting the propagator can be derived from a single deterministic path rather than summing over many paths.

Contribution

It introduces a novel physical interpretation of the phase in Feynman path integrals, linking it to time reversal and deterministic paths, challenging the traditional mathematical view.

Findings

The phase in Feynman path integrals can originate from time reversal.

A single deterministic path can produce the propagator.

The traditional sum-over-paths approach can be reinterpreted physically.

Abstract

In the path integral formulation of quantum mechanics, the phase factor Exp[iS(x[t])] is associated with every path x[t]. Summing this factor over all paths yields Feynman's propagator as a sum-over-paths. In the original formulation, the complex phase was a mathematical device invoked to extract wave behaviour in a particle framework. In this paper we show that the phase itself can have a physical origin in time reversal, and that the propagator can be drawn by a single deterministic path.