Back-Reaction In Lightcone QED

Abstract

We consider the back-reaction of quantum electrodynamics upon an electric field E(x_+) = - A'_-(x_+) which is parallel to x^3 and depends only on the lightcone coordinate x_+ = (x^0 + x^3)/\sqrt{2}. Novel features are that the mode functions have simple expressions for arbitrary A_-(x_+), and that one cannot ignore the usual lightcone ambiguity at zero + momentum. Each mode of definite canonical momenta k_+ experiences pair creation at the instant when its kinetic momentum p_+=k_+ - e A_-(x_+) vanishes, at which point operators from the surface at x_- =-\infty play a crucial role. Our formalism permits a more explicit and complete derivation of the rate of particle production than is usually given. We show that the system can be understood as the infinite boost limit of the analogous problem of an electric field which is homogeneous on surfaces of constant x^0.