Integral representations of the star product corresponding to the -ordering of the creation and annihilation operators
arXiv:1802.04213 · doi:10.1088/0031-8949/90/7/074008
Abstract
A new integral representation is obtained for the star product corresponding to the -ordering of the creation and annihilation operators. This parametric ordering convention introduced by Cahill and Glauber enables one to vary the type of ordering in a continuous way from normal order to antinormal order. Our derivation of the corresponding integral representation is based on using reproducing formulas for analytic and antianalytic functions. We also discuss a different representation whose kernel is a generalized function and compare the properties of this kernel with those of the kernels of another family of star products which are intermediate between the and -quantization.
LaTeX, 17 pages, invited contribution to special issue of "Physica Scripta" in honour of the 75th birthdays of Margarita and Vladimir Man'ko, matches version accepted for publication, with minor typos corrected