The Angular Momentum Dilemma and Born-Jordan Quantization

TL;DR

This paper argues that Born-Jordan quantization is the correct approach for phase space quantum mechanics, resolving the angular momentum dilemma and ensuring equivalence between Schrödinger and Heisenberg pictures.

Contribution

It demonstrates that Born-Jordan quantization replaces Weyl quantization for consistency in phase space quantum mechanics and resolves longstanding angular momentum issues.

Findings

Born-Jordan quantization ensures Schrödinger-Heisenberg equivalence.

The angular momentum dilemma is resolved with Born-Jordan quantization.

A new phase space distribution replaces the Wigner distribution.

Abstract

We have shown in previous work that the rigorous equivalence of the Schr\"odinger and Heisenberg pictures requires that one uses Born-Jordan quantization in place of Weyl quantization. It also turns out that the so-called Dahl-Springborg angular momentum dilemma disappears if one uses Born--Jordan quantization. These two facts strongly suggest that the latter is the only true quantization procedure, and this leads to a redefinition of phase space quantum mechanics, where the usual Wigner distribution has to be replaced with a new distribution.