Hall Coefficient in an Interacting Electron Gas

The Hall conductivity in a weak homogeneous magnetic field, $\omega_{c}\tau \ll 1$,iscalculated\mathrm{.}Wehaveshownthattoleadingorderin$1/\epsilon_{F}\tau$theHallcoefficient$R_{H}$ is not renormalized by the electron-electron interaction. Our result explains the experimentally observed stability of the Hall coefficient in a dilute electron gas not too close to the metal-insulator transition. We avoid the currently used procedure that introduces an artificial spatial modulation of the magnetic field. The problem of the Hall effect is reformulated in a way such that the magnetic flux associated with the scattering process becomes the central element of the calculation.