Abstract
An approximation scheme for the one-nucleon Green's functions previously put forward by the authors is renormalized. The experimental mass and the constants ${Z}_{1}$ and ${Z}_{2}$ are rigorously expressed as free-particle limits of integrals over the kernels appearing in the scheme. The mass and wave-function renormalization are carried out rigorously; the vertex renormalization is performed by a slight redefinition of the approximation scheme, without greatly altering the physical assumptions peculiar to each approximation. General prescriptions for renormalization are written down, and the first three approximations are explicitly shown to be finite.
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