The role of inequalities in the analysis of many-body systems

摘要

We discuss the strategy of determining properties of many-body systems by applying successively more stringent limitations on the domain on which solutions can lie, i.e., sharpening the degree of resolution of the results obtained. A rough division is made into universal, or system-independent inequalities and systemdependent ones, which are joined by equalities or sum rules. General examples include Fermion ground states and classical fluids in thermal equilibrium, and for the latter, the effect of estimation by saturating inequalities.