CONSISTENCY OF APPROXIMATION SCHEMES IN MANY-BODY THEORY

Many functions of physical interest are defined by means of recursion relations where a function of a given rank can be expressed in terms o f the functions of lower rank. It is also usually possible to define a pproximation schemes which, with natural modifications, can be applied to evaluate any function of the hierarchy. Typical examples are densi ty functions, propagators, and Green's functions, and the approximatio n approaches to them are often based on perturbation theory. The attem pt of this work is to clarify the connection between the approximation schemes for propagators and the hierarchy of linking equations. The c oncept of scheme consistency is introduced and used to extend availabl e approximation schemes. As a specific example the theory is worked ou t for the particle-particle propagator, a quantity describing the simu ltaneous removal of two particles from a many-particle system. It is e xpected that the derived working equations are of importance in the de scription of double-ionization processes where each of the two removed electrons originates from a different part of the system.