The jump in generality made by Leray for the WKB type construction of high frequency asymptotic solutions of linear partial differential equations has allowed the treatment of arbitrary linear systems of partial differential equations. It also permitted the extension to quasilinear systems, and the appearance of new properties linked to the non linearities, in particular a distorsion of signals. The non linearity of a differential system is also an obstruction to the existence of global solutions of evolution problems. In the case of non linear wave equations on the Minkowski spacetime of dimension 4 it has been discovered by Christodoulou and Klainerman that a “null condition” satisfied by the non linearities leads to global existence results. The equations of the fundamental field equations (standard model, Einstein equations) are quasi linear second order partial differential equations, but not well posed due to gauge invariance. We introduce a “polarized null condition”. We show it is satisfied by the standard model, but not quite by the Einstein equations. We construct for both systems asymptotic high frequency solutions with linear transport law along the rays. In the case of Einstein equations the wave inflicts a “back reaction” on the background metric.