Born-Jordan Quantization and the Uncertainty Principle

TL;DR

This paper explores the Born-Jordan quantization scheme, highlighting its differences from Weyl quantization, especially regarding the uncertainty principle's symplectic covariance, and discusses its recent revival in time-frequency analysis.

Contribution

It provides an analysis of the Born-Jordan quantization's properties and contrasts it with Weyl quantization, emphasizing its unique features and recent applications.

Findings

Uncertainty principle lacks full symplectic covariance in Born-Jordan scheme.

Born-Jordan quantization differs from Weyl in key mathematical properties.

Recent revival of Born-Jordan in time-frequency analysis contexts.

Abstract

The Weyl correspondence and the related Wigner formalism lie at the core of traditional quantum mechanics. We discuss here an alternative quantization scheme, whose idea goes back to Born and Jordan, and which has recently been revived in another context, namely time-frequency analysis. We show that in particular the uncertainty principle does not enjoy full symplectic covariance properties in the Born and Jordan scheme, as opposed to what happens in the Weyl quantization.