Born-Jordan pseudodifferential operators and the Dirac correspondence: Beyond the Groenewold-van Hove theorem

In this work we show that the above commutator rule in fact holds for the Born-Jordan quantization, at least for symbols of the type f(x)+g(ξ). Moreover we will prove that, remarkably, this property completely characterizes this quantization rule, making it the quantization which best fits the Dirac dream.