Study of a Two-Dimensional Electron Gas in a Weak Magnetic Field.

A many-body theory of a two-dimensional electron gas in a magnetic field is presented. The field dependence of the Fermi momentum shows a 2-D peculiarity. It consists of the spin-dependent paramagnetic part and the orbital diamagnetic part. The former increases more strongly with r sub s than the latter. The para- and dia-magnetic susceptibilities are found as functions of r sub s. The field-dependent ground state energy is evaluated. Its paramagnetic part decreases steadily with r sub s, while the diamagnetic part shows a maximum. No such a maximum was found for the 3D case in the same approximation which is valid for high density and low magnetic fields. From the susceptibilities, an effective g factor and an effective mass are derived.