| We present a theory of the Kondo problem in terms of a renormalization group theory (RG) for the energy dependent dimensionless coupling function g(ω) and the spin relaxation rate Γ. At low energies, the RG β-function is proportional to, respectively, g3 at strong, and g2 at weak coupling. The RG flow is cut off by the spin relaxation rate Γ. We determine Γ self-consistently and show that Γ=TK+ O(T2) as the temperature T→0 (here TK is the Kondo temperature). As a consequence, g at the Fermi energy (ω→0) is found to diverge as 1/T , which allows to classify the diagrams contributing to, e.g., the local spin self-energy and the conductance. The linear response conductance is found to obey unitarity, G=1-O(T2) and agrees well with Numerical RG results. The spin-susceptibility is found to be in agreement with Bethe ansatz results. |
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