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We present a full ab-inito description of the coupled out-of-equilibriumdynamics of photons, phonons, and electrons. In the present approach thequantised nature of the electromagnetic field as well as of the nuclearoscillations is fully taken into account. The result is a set ofintegro-differential equations, written on the Keldysh contour, for the Green'sfunctions of electrons, phonons, and photons where the different kind ofinteractions are merged together. We then concentrate on the electronicdynamics in order to reduce the problem to a computationally feasible approach.By using the Generalised Baym-Kadanoff ansatz and the Completed Collisionapproximation we introduce a series of efficient but controllableapproximations. In this way we reduce all equations to a set of decoupledequations for the density matrix that describe all kind of static and dynamicalcorrelations. The final result is a coherent, general, and inclusive scheme tocalculate several physical quantities: carrier dynamics, transientphoto-absorption and light-emission. All of which include, at the same time,electron-electron, electron-phonon, and electron-photon interaction. We furtherdiscuss how all these observables can be easily calculated within the presentscheme using a fully atomistic ab-initio approach.

An unified theory of quantised electrons, phonons and photons  out-of-equilibrium: a simplified {\em ab-initio} approach based on the  Generalised Baym-Kadanoff ansatz