Free Electron Laser Theory Using Two times Green Function Formalism

In this paper, we present a quatum theory for free electron laser obtained by firstly using the Two time’s Green Function method developed by Matsubara for solid physics theory. The dispersion relation for the laser photon obtained is limited to the case of low intensity of the laser due to the decoupling the correlation function in low order. For the analysis of the self-amplified emission (SASE), the high intensity laser radiation which strongly affect the trajectory of the free electron is involved, the use of the classical approximation for laser can formulate the laser radiation with multiple frequency. To get the quantum effects in the high intensity laser, use of the perturbation theory, and the expansion methods of state function using the coherent, squeeze and super-radiant states have discussed.