Fumi’s theorem in conjunction with some general theorems associated with auxiliary particle methods dictates the functional form of the on-shell auxiliary particle self-energy Σ for a certain class of impurity scattering problems. An explicit calculation which confirms the result is described and the implications for various approaches to the Kondo effect discussed.
Barnes, S. E., "Implications of Fumi’s Theorem for Auxiliary Particle Methods" (1995). Physics Articles and Papers. 75.