Composite operators and algebra constraints: a formalism for highly interacting systems

TL;DR

This paper introduces a formalism for analyzing highly interacting electronic systems using composite operators and algebra constraints, reformulating Green's functions to account for complex interactions and symmetries.

Contribution

It develops a novel perturbation scheme based on composite operators and algebra constraints, enhancing the analysis of strongly interacting systems.

Findings

Reformulation of Green's functions with algebra constraints

Promotion of composite operators as fundamental fields

Application to highly interacting electronic systems

Abstract

A formalism for the study of highly interacting electronic systems is presented. The proposed scheme is based on two key concepts: composite operators and algebra constraints. Composite field operators, that naturally appear as a consequence of interaction, are promoted to the rank of basic fields in terms of which a perturbation formulation is set up. The formalism is based on the use of Green's function and equation of motion method. The use of composite operators requires a revisitation of the Green's function formulation, where the representation is determined by means of algebra constraints which are a manifestation at macroscopic level of the algebra rules and symmetry properties obeyed at microscopic level.