Current conservation and resistance fluctuations in a four probe geometry

The mean square variation in the magnetoresistance of small disordered metal wires is calculated in a four probe geometry with leads much longer than a dephasing length. Dephasing scattering is included through a two body interaction using standard techniques from many body theory. As a result, only a region within approximately a dephasing length of the sample contributes to the resistance fluctuations. Throughout the paper particular emphasis is given to current conservation, which is guaranteed by explicitly producing a set of current conserving diagrams and then evaluating them in the limits appropriate to experiment.