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