Configuration Space Methods for the Construction of Potentials

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Abstract
Methods proposed recently by Lévy and by Brueckner and Watson for the construction of potentials in quantum field theory by superficially dissimilar techniques are rederived on a unified basis, that of the underlying equations in Fock space. It is supposed that certain amplitudes contained in the state vector are of primary physical interest, and it is demonstrated that the two methods differ essentially only in the order of elimination of the remaining amplitudes. The interpretation and practical use of the methods is discussed in a formal way, with emphasis on problems of consistency which limit the utility of the techniques. Elementary examples are discussed in the appendixes.