A revised diagrammatic technique for the degenerate Anderson model

The Goldstone diagrammatic technique developed by Keiter and Kimball for single impurity Anderson model is reformulated. Instead of having the self_energy functions defined on the real axis as the Brillouin_Wigner theory, we have defined the functions on the complex plane. This avoids the complicated and cumbersome regularization procedure required in the Keiter and Kimball formulation. Most important of all it makes the numerical calculations possible. The exact partition function may be written down in terms of irreducible self_energy diagrams. The Green function and spectral function are derived.