  We derive the covariant formalism associated with the relativistic
Sunyaev-Zel'dovich effect due to a non-thermal 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 (and widely used in
the literature) to compute the inverse Compton scattering of a population of
relativistic electrons on CMB photons, can actually be re-interpreted as a
Boltzmann-like equation, in the single scattering approximation.
