Born–Jordan quantization and the uncertainty principle

The Weyl correspondence and the related Wigner formalism lie at the core of traditional quantum mechanics. We discuss here an alternative quantization scheme, the idea of which goes back to Born and Jordan, and which has recently been revived in another context, namely time–frequency analysis. We show in particular that 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. (paper)