Renormalization and scaling in the X-ray absorption and Kondo problems

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Abstract
The renormalization group method is extended in the case of logarithmic problems to include the imaginary parts of Green function and vertices which have been neglected in the earlier versions of the theory. The relationship between multiplicative renormalization absorption and Kondo problems. The properly defined invariant couplings depend on a single variable, the scaling energy, and are real, as expected physically. The scaling laws are rederived on this more rigorous basis. It is shown that the imaginary parts of the Green functions and vertices give no contribution to the scaling laws.