A path integral approach to Anderson-Holstein model

The Anderson-Holstein model is studied in the framework of the semiclassical approximation. Analytic results for Kondo temperature renormalized by weak electron-phonon interaction and for phonon Green function are obtained, and they are interpreted from the viewpoint of dynamical mean field theory. Especially the isotope effect of the effective electron mass is discussed in the presence of strong electron correlation. The results are also compared with those by numerical renormalization group and other related works, and they are consistent with each other in their common domain of validity.