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 $\delta \sigma$ and show that the effective decoherence length extracted from $\delta \sigma$ remains finite down to $T=0\mathrm{}$ due to electron-electron interactions.