Time-retarded interactions in systems with tunneling states and strong electron-phonon coupling

A path integral approach to the problem of the time-retarded interactions between tunneling states and fermionic excitations in systems with strong electron-phonon coupling is presented. The full partition function is derived up to third order in the coupling constant and the interaction strengths, which weigh both the attractive and the repulsive forces, are renormalized as a function of temperature. The conditions for localization of polarons in double well potentials related to the tunneling states are discussed. The model is applied to evaluate the contribution to the electrical resistivity in systems with structural lattice instabilities