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Semiclassical methods are used to study the nonlinear interaction of light invacuum in the context of four wave mixing. This study is motivated by a desireto investigate the possibility of using recently developed powerful ultrashort(femtosecond) laser pulses to demonstrate the existence of nonlinear effects invacuum, predicted by quantum electrodynamics (QED). An approach, similar toclassical nonlinear optics in a medium, is developed in this article. Athird-order nonlinear effective susceptibility of vacuum is then introduced.

Four-wave interaction in gas and vacuum: definition of a third-order nonlinear effective susceptibility in vacuum: $\chi$ vacuum(3)