Gauge-invariant theory of the Hall effect in a weak magnetic field

Abstract

An exact expression is obtained for the off-diagonal part of the conductivity tensor of a man-body electron system up to the first order in an applied magnetic field. The formalism includes all types of electron scattering mechanism and is independent of the choice of the gauge describing the magnetic field. The resulting formula is expressed in terms of the three-body correlation function and includes the Lorentz force in an explicit operator form.