  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.
