Derivation of exact results for the single-ion Kondo problem with the use of diagrammatic methods

It is shown that exact results for the single-impurity Kondo problem can be obtained by diagrammatic methods. The results for the susceptibility and specific heat agree with those obtained by Wilsons numerical methods. In particular, the crossover W=(/e)1/2 and Wilson R=2 ratios are reproduced exactly. Conduction-electron scattering from the impurity reaches the unitarity limit corresponding to a phase shift =/2. Both this and the compensation of the impurity spin are also exact results. The methods described are relatively easily extended to the Anderson model and the corresponding lattice problems.