Auxiliary systems for observables: dynamical local connector approximation for electron addition and removal spectra

This thesis proposes an innovative theoretical method for studying one-electron excitation spectra. We propose two shortcuts to the standard method, which relies on complex, non-local self energies evaluated specifically for each material. The first one is the introduction of an auxiliary system that exactly targets, in principle, the excitation spectrum of the real system, via a local and frequency-dependent, yet real, potential (the spectral potential). The second shortcut consists in calculating this potential just once and forever in a model system, the homogeneous electron gas. To study real materials, we design a connector which prescribes the use of the gas results for calculating electronic spectra. We propose an approximation for it, based on local properties of the system: the dynamical local connector approximation. We implement this procedure for four prototypical materials: sodium, aluminum, silicon and argon. The spectra we obtain demonstrate the potential of this theory.