On moment conserving decoupling techniques for electron propagators

Moment-conserving decoupling procedures for the one-electron Green's function (electron propagator) are investigated. By analysis of one particular system (Hubbard model) it becomes clear that the momentconserving techniques so far proposed for interacting systems are all special cases of [l, 0], [2, 1], or [3, 2] Padè approximants differing only in which terms they omit, how they define self-consistency, and which operator algebra they utilize. The number of formally conserved moments appears not to be a particularly useful criterion of the accuracy of a decoupling procedure, since a two-moment scheme ( HartreeFock) may be numerically closer to the exact answer than some three-moment procedures. Use of the complete Fade approximant, as suggested by Lukman and Goscinski for the particle-hole propagator, appears to be the most consistent method.