One of the simplest, yet most striking, outcomes of electron correlation is the exciton. The creation of electron-hole pair(s), under external perturbation, is an intrinsic collective excitation of the system and, from the theoretical point of view, is defined in terms of 'beyond single-particle'. In this contribution I will illustrate the importance of exciton dispersion, how it is necessary to go beyond the dipole approximation and how this can be used in a variety of experiments: Electron Energy Loss, Inelastic Xray scattering, etc.
In a second part, I will analyse the new frontiers that the exciton dispersion open, both in terms of general analysis tool and in terms of new spectroscopic features (in RIXS, in Photoemission, etc.).
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