Basics of Resonant Elastic X-ray Scattering theory

We recall the basic equations of Resonant Elastic X-ray Scattering (REXS), starting from the photon-electron Hamiltonian interaction, and describing the different components for the possible transitions. We also make the connection with classical physics and we emphasize the signs of the relevant terms, resonant and non resonant, to comply to the convention on the phase wave