Quantum decoherence and weak localization at low temperatures

With the aid of the Keldysh technique we develop a path-integral formalism which allows us to nonperturbatively study the quantum dynamics of electrons in a disordered metal in the presence of interactions. We derive a formally exact equation of motion for the electron density matrix and demonstrate that the effect of interaction of the electron with other electrons in a disordered metal is equivalent to that of an effective dissipative environment. We obtain nonperturbative results for the weak localization correction to the conductance δσ and show that the effective decoherence length extracted from δσ remains finite down to $T=0$ due to electron-electron interactions.