$g$ Factor of the Two-Dimensional Interacting Electron Gas

The $g$ factor of quasiparticle states near the Fermi energy in a two-dimensional electron gas with Coulomb interactions is calculated in a static approximation. It is argued that this quadiparticle $g$ factor, different from the free-electron $g=2.0023\mathrm{}$, is the relevant quantity for spin splittings in experiments such as those on de Haas-van Alphen or magnetoconductivity oscillations, and, in particular, in experiments on electrons in silicon surface inversion layers. The $g$ factor observed in conduction-electron spin resonance, on the other hand, should be the bulk value of 1.99.