Quantization from Hamilton-Jacobi theory with a random constraint

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 $\pm \hslash /2$ with equal probability.

6 pages, accepted for publication in Physica A

References in corpus (5)

• Quantization Methods: A Guide for Physicists and Analysts
• Grounding Bohmian Mechanics in Weak Values and Bayesianism
• Curie-Weiss model of the quantum measurement process
• Quantum fluctuations as deviation from classical dynamics of ensemble of trajectories parameterized by unbiased hidden random variable
• Possible corrections to quantum mechanical predictions in hidden variable model

Cited by in corpus (6)

• Quantum mechanics as classical statistical mechanics with an ontic extension and an epistemic restriction
• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• Geometric Hamilton-Jacobi theory for systems with external forces
• Quantization from an exponential distribution of infinitesimal action
• Objective uncertainty relation with classical background in a statistical model
• Quantum dynamics and kinematics from a statistical model selected by the principle of Locality