Commutation relations for simplest symmetric ordering of position and inverse momentum operators

Abstract

Quantization under simplest symmetric ordering of classical monomials with negative integral exponents of momentum has been written in integral form. This integral representation not only proved useful in transforming Weyl quantization to symmetric ordering quantization, and vice versa. They also facilitate derivation of commutation relations among different operators involving inverse powers of momentum operator, relations which can be used in solving quantization problems for classical functions with singularity along the momentum axis.