Generalized hedin's equations for quantum many-body systems with spin-dependent interactions

Hedin's equations for the electron self-energy and the vertex have originally been derived for a many-electron system with Coulomb interaction. In recent years, it has been increasingly recognized that spin interactions can play a major role in determining physical properties of systems such as nanoscale magnets or of interfaces and surfaces. We derive a generalized set of Hedin's equations for quantum many-body systems containing spin interactions, e.g., spin-orbit and spin-spin interactions. The corresponding spin-dependent GW approximation is constructed.