Griffiths Inequalities for Fermion Systems

Abstract

A discussion is presented of the use of G-matrix restrictions to reduce fermion lower bound principles to dependence upon the 1-body d. matrix alone. This suggests the utility of something of the form of Griffiths inequalities, whose classical version was reviewed, emphasizing the role of replica systems and tailored representations for painless realization of correlations. The BCS Hamiltonian, as well as its replica pair, can be treated in analogous fashion, producing a large set of correlation inequalities. These are not quite sufficient to solve the G-matrix-reduced BCS Hamiltonian. A similar redn. technique is applied to the case of an e plasma, and suggestions made as to the nature of Griffiths-type inequalities which might be available for similar systems.