Green's-function diagrammatic technique for complicated level systems

Abstract

A Green's function theory applicable to magnetic systems with complicated levels for each ion is developed using the standard basis operators. A diagrammatic technique is employed. This provides a self-consistent approach to the rare-earth and actinide systems where the crystal field is of the same order as the exchange interaction. A Wick-like theorem is shown first followed by a discussion of the diagrammatic representation. Guided by a priority rule we consider all possible vertices. Rules for construction and evaluation of diagrams are given and summation of diagrams is discussed.