Study of resonant inelastic light scattering in Keldysh-Schwinger functional integral formalism

The scattering cross section of the resonant inelastic light scattering is represented as a correlation function in the Keldysh-Schwinger functional integral formalism. The functional integral approach enables us to compute the cross section in the Feynman diagram perturbation theory where many-body effects can be fully incorporated. This approach is applied to the one G-phonon Raman scattering of graphene, and the result is shown to agree with the one previously obtained by the conventional Fermi golden rule formula. Also, this approach is generalized to the systems in non-equilibrium conditions.