Bridging nano-optics and condensed matter formalisms in a unified description of inelastic scattering of relativistic electron beams

In the last decades, blossoming of experimental breakthroughs in domain electron energy loss spectroscopy (EELS) has triggered a variety theoretical developments. Those have to deal with completely different situations, from atomically resolved phonon mapping circular dichroism passing by surface plasmon mapping. All them rely on very physical approximations and not yet been reconciled, despite early attempts do so. As an effort that direction, we report development scalar relativistic quantum electrodynamic (QED) approach inelastic scattering fast electrons. This theory can be adapted describe all modern EELS experiments, under relevant approximations, reduced most theories. aim, present this paper state art basics QED scattering. We then give clear relation between two once antagonist descriptions EELS, retarded dyadic Green function, usually applied photonic excitations quasi-static mixed dynamic form factor (MDFF), more core electronic material. Using photon propagator material, expressed gauges, as tool understand interaction extend newly defined quantity, MDFF. The function MDFF does depend only specifics particle (here, electron) probing target. Therefore, it any where electromagnetic properties material is needed. use establish important EELS-related equations. first one relates spatially imaginary part incoming outgoing beam wavefunction, synthesizing common theories developed for analyzing experiments. second shows evolution density matrix proportional mutual coherence tensor, proving quite universally, correlations target are imprinted beam.