Short-time path integral approximation supports Born-Jordan quantization only for quadratic-momentum Hamiltonians with constant mass; Weyl rule agrees for that class.
De Gosson, (2018) Short-Time Propagators and the Born–Jordan Quantization Rule, Entropy, 20(11), 869
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Is Born-Jordan really the universal Path Integral Quantization Rule?
Short-time path integral approximation supports Born-Jordan quantization only for quadratic-momentum Hamiltonians with constant mass; Weyl rule agrees for that class.