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arXiv · 1802.04213

Integral representations of the star product corresponding to the $s$-ordering of the creation and annihilation operators

Michael A. Soloviev
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Abstract

A new integral representation is obtained for the star product corresponding to the $s$-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 $qp-$ and $pq$-quantization.

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Michael A. Soloviev. 2018-02-12. Integral representations of the star product corresponding to the $s$-ordering of the creation and annihilation operators. https://doi.org/10.1088/0031-8949%2F90%2F7%2F074008

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