Effects of electron-electron collisions with small energy transfers on quantum localisation

The effect of electron-electron collisions with small energy transfers on the quantum electron localisation has been studied. It is shown that in one and two dimensions such collisions determine the temperature dependence of the conductivity. In three dimensions the contribution of processes with small energy transfers is less than that of the usual electron-electron collisions, in which the energy transfer is of the order of the temperature T. The criterion for the quasiparticle description of electrons in metals in different dimensions is discussed. It is shown that for d>or=2 this description is valid, while for d=1 it is not correct. The effect of noise in the external circuit on quantum corrections to the conductivity is studied.