Is Born-Jordan really the universal Path Integral Quantization Rule?

TL;DR

This paper critically examines the universality of the Born-Jordan quantization rule, revealing its limitations to specific Hamiltonian classes and comparing it with other schemes like Weyl quantization.

Contribution

The authors challenge the prevailing view by showing that the short-time propagator asymptotic expansion applies only to quadratic Hamiltonians, questioning the Born-Jordan rule's universality.

Findings

The asymptotic expansion applies only to Hamiltonians quadratic in momentum with constant mass.

Born-Jordan rule aligns with these Hamiltonians, but other rules like Weyl give the same results.

The universality of the Born-Jordan rule is limited to specific Hamiltonian classes.

Abstract

It has been argued that the Feynman path integral formalism leads to a quantization rule, and that the Born-Jordan rule is the unique quantization rule consistent with the correct short-time propagator behavior of the propagator for non-relativistic systems. We examine this short-time approximation and conclude, contrary to prevailing views, that the asymptotic expansion applies only to Hamiltonian functions that are at most quadratic in the momentum and with constant mass. While the Born-Jordan rule suggests the appropriate quantization of functions in this class, there are other rules which give the same answer, most notably the Weyl quantization scheme.