Ordered operator expansions and reconstruction from ordered moments

Abstract

The structure of ordered expansions in powers of boson operators and of canonical operators and the dual problem of operator reconstruction from ordered moments is derived and applied to the complete Gaussian class of ordering. In particular, the interpolation lines between normal and antinormal ordering and between standard and antistandard ordering with Weyl symmetrical ordering in their centre are dealt with in detail. The auxiliary operators for expansions in symmetrical ordering are explicitly found in the Fock-state representation and in other different representations. General and specialized formulae are derived for different ordering of powers of linear combinations of boson and of canonical operators which involve Hermite polynomials of operators. The link between symmetrical ordering of powers of boson operators and of canonical operators is expressed by means of Jacobi polynomials. Some basic formulae of operator ordering and operator expansion are collected for convenient use in the appendix.