  We propose a new semiclassical approach based on the dynamical mean field
theory to treat the interactions of electrons with local lattice fluctuations.
In this approach the classical (static) phonon modes are treated exactly
whereas the quantum (dynamical) modes are expanded to second order and give
rise to an effective semiclassical potential. We determine the limits of
validity of the approximation, and demonstrate its usefulness by calculating
the temperature dependent resistivity in the Fermi liquid to polaron crossover
regime (leading to `saturation behavior') and also isotope effects on
electronic properties including the spectral function, resistivity, and optical
conductivity, problems beyond the scope of conventional diagrammatic
perturbation theories.
