Résumé
We derive the covariant formalism associated with the relativistic Sunyaev-Zel'dovich effect due to a nonthermal population of high energy electrons in clusters of galaxies. More precisely, we show that the formalism proposed by Wright in 1979, based on an empirical approach to compute the inverse Compton scattering of a population of relativistic electrons on CMB photons, can actually be reinterpreted as a Boltzmann-like equation, in the single scattering approximation.