Moyal Bracket and Ehrenfest’s Theorem in Born–Jordan Quantization

Abstract

The usual Poisson bracket { A , B } can be identified with the so-called Moyal bracket { A , B } M for larger classes of symbols than was previously thought, provided that one uses the Born–Jordan quantization rule instead of the better known Weyl correspondence. We apply our results to a generalized version of Ehrenfest’s theorem on the time evolution of averages of operators.