Berry Phase in a Bloch-Like Sphere for Nonlinear Compton Scattering

We use a Bloch-like representation for nonlinear Compton scattering in order to derive the energy conservation inside the Dirac-Delta argument. For this end is argued that a geodesic translation along the Bloch-like sphere would be perceived as the cause of the apparition of harmonics fact that it supports through the existence of phases seen as angles on the spherical system. The displacement along the sphere is perceived as a path that creates the well-known Berry's phase. The adiabatic mechanism might be responsible on the multiple absorption and emission of photons by a free electron under the interaction with a super-intense laser.