  Inelastic low-energy Raman and high-energy X-ray scatterings have made great
progress in instrumentation to investigate the strong electronic correlations
in matter. However, theoretical study of the relevant scattering spectrum is
still a challenge. In this article, we present a Schwinger-Keldysh canonical
perturbation formalism for the electronic Raman scattering, where all the
resonant, non-resonant and mixed responses are considered uniformly. We show
how to use this formalism to evaluate the cross section of the electronic Raman
scattering off an one-band superconductor. All the two-photon scattering
processes from electrons, the non-resonant charge density response, the elastic
Rayleigh scattering, the fluorescence, the intrinsic energy-shift Raman
scattering and the mixed response, are included. In the mean-field
superconducting state, Cooper pairs contribute only to the non-resonant
response. All the other responses are dominated by the single-particle
excitations and are strongly suppressed due to the opening of the
superconducting gap. Our formalism for the electronic Raman scattering can be
easily extended to study the high-energy resonant inelastic X-ray scattering.
