Two-Scale Analysis of the $\mathrm{SU}\left(\mathit{N}\right)$ Kondo Model

We show how to resolve coherent low-energy features embedded in a broad high-energy background by use of a fully self-consistent calculation for composite particle operators. The method generalizes the formulation of Roth, which linearizes the dynamics of composite operators at any energy scale. Self-consistent equations are derived and analyzed in the case of the single-impurity $\mathrm{SU}\left(N\right)$ Kondo model.