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Quantum electrodynamics in a laser and the electron laser collision

Quantum electrodynamics in a laser is formulated, in which the electron-laser interaction is exactly considered, while the interaction of an electron and a single photon is considered by perturbation. The formulation is applied to the electron-laser collisions. The effect of coherence between photons in the laser is therefore fully considered in these collisions. The possibility of $γ-$ray laser generation by use of this kind of collision is discussed.