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We have shown in previous work that the equivalence of the Heisenberg andSchr\"odinger pictures of quantum mechanics requires the use of the Born andJordan quantization rules. In the present work, we give further evidence thatthe Born--Jordan rule is the correct quantization scheme for quantum mechanics.For this purpose, we use correct short-time approximations to the actionfunctional, which lead to the desired quantization of the classicalHamiltonian. We thus prove that a previous argument of Kerner and Sutcliffe,refuted by Cohen, is correct.

Short-Time Propagators and the Born--Jordan Quantization Rule