Short-Time Propagators and the Born--Jordan Quantization Rule

TL;DR

This paper provides further evidence supporting the Born--Jordan quantization rule as the correct scheme in quantum mechanics by using accurate short-time approximations to the action functional.

Contribution

It demonstrates that the Born--Jordan rule is consistent with the short-time propagator approach, reaffirming its validity over alternative quantization methods.

Findings

Born--Jordan rule aligns with short-time propagator approximations

Confirms previous refuted argument by Kerner and Sutcliffe

Supports the Born--Jordan rule as the correct quantization scheme

Abstract

We have shown in previous work that the equivalence of the Heisenberg and Schr\"odinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work, we give further evidence that the Born--Jordan rule is the correct quantization scheme for quantum mechanics. For this purpose, we use correct short-time approximations to the action functional, which lead to the desired quantization of the classical Hamiltonian. We thus prove that a previous argument of Kerner and Sutcliffe, refuted by Cohen, is correct.