\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
To probe the nonlinear effects of photon-photon interaction in the quantum electrodynamics, we study the generation of circular polarized photons by the collision of two linearly polarized laser beams. In the framework of the Euler-Heisenberg effective Lagrangian and the Quantum Boltzmann equation for the time evolution of the density matrix of polarizations, we calculate the intensity of circular polarizations generated by the collision of two linearly polarized laser beams and estimate the rate of generation. As a result, we show that the generated circular polarization can be experimentally measured, on the basis of optical laser beams of average power KW, which are currently available in laboratories. Our study presents a valuable supplementary to other theoretical and experimental frameworks to study and measure the nonlinear effects of photon-photon interaction in the quantum electrodynamics.
\end{document}