Quantization from Hamilton-Jacobi theory with a random constraint

TL;DR

This paper introduces a novel quantization method derived from Hamilton-Jacobi theory incorporating a random constraint, which reproduces canonical quantization results with a unique operator ordering under specific conditions.

Contribution

It presents a new quantization approach based on Hamilton-Jacobi theory with a random constraint, linking the Lagrange multiplier to quantum operator ordering.

Findings

Reproduces canonical quantization results

Operator ordering is uniquely determined by the Lagrange multiplier

Lagrange multiplier takes binary values ±ħ/2 with equal probability

Abstract

We propose a method of quantization based on Hamilton-Jacobi theory in the presence of a random constraint due to the fluctuations of a set of hidden random variables. Given a Lagrangian, it reproduces the results of canonical quantization yet with a unique ordering of operators if the Lagrange multiplier that arises in the dynamical system with constraint can only take binary values $\pm\hbar/2$ with equal probability.