Quantization from an exponential distribution of infinitesimal action

TL;DR

This paper proposes a statistical model of quantization using an exponential distribution of infinitesimal action, linking the Planck constant to average deviations from stationary action.

Contribution

It introduces a novel probabilistic framework for quantization based on exponential laws of infinitesimal action deviations.

Findings

Trajectory deviations follow an exponential distribution

Planck constant relates to average deviation from stationary action

Model provides a new perspective on quantum behavior

Abstract

A statistical model of quantization based on an exponential distribution of infinitesimal action is proposed. Trajectory which does not extremize the action along an infinitesimal short segment of path is allowed to occur with a very small probability following an exponential law. Planck constant is argued to give the average deviation from the infinitesimal stationary action.