Conservation of the spectral moments in the n-pole approximation

TL;DR

This paper introduces a general Green's function formulation in the n-pole approximation, demonstrating spectral moment conservation up to a specific order, applicable across various models.

Contribution

It provides a model-independent scheme for calculating Green's functions and proves a theorem on spectral moment conservation within the n-pole approximation.

Findings

Spectral moments are conserved up to order 2(n-l+1).

The method is general and does not depend on specific models.

Comparison with spectral density approach is discussed.

Abstract

A formulation of the Green's function method is presented in the n-pole approximation. Without referring to a specific model we give a general scheme of calculations that easily permits the computation of the "single-particle" Green's function in terms of the energy matrix. A theorem is proved which states that the moments of the spectral density function are conserved up to the order 2(n-l+1), where l is the order of the composite field. A comparison with the spectral density approach is also discussed.