A moment theorem for resonance line shapes arising from decoupled Green's function equations

A theorem is derived which enables one to bypass quadrature in the calculation of moments of a resonance line obtained from any decoupling of the Green's function hierarchy of equations. These moments are those of the resonance line as expressed in terms of delta-function peaks prior to smearing. A comparison with exact theoretical moments then provides a test of the decoupling procedure as distinct from the smearing technique. The method is illustrated by application to the one-dimensional Ising model.