Accurate evaluation of the conditions for generation of quantum effects in relativistic interactions between laser and electron beams

Abstract

The quantum behavior of the system composed of an electron in an electromagnetic field is described by the Dirac equation, whose solution is a wave function represented by a column matrix with four components. We prove, without using any approximation, that these components can be put in a form which reveals directly the values of the electron energy, laser beam intensity, or amplitude of the electric field intensity, for which the quantum electrodynamics effects are generated. Our results are in good agreement with the experimental data reported in the literature. We prove that the four components of the wave function verify the continuity equation of quantum electrodynamics. Our treatment is in good agreement with the Compton relation. We show that the interaction of electrons with laser beams could be modeled using classical approaches regardless of the laser beam intensity as long as the electrons are non-relativistic, in agreement with published experimental data.