Null-plane quantum electrodynamics in an external radiation field

Abstract

The formalism developed in this paper is designed to treat the interaction of an electron with a laser pulse. Precisely, it is a formulation on null hyperplanes of quantum electrodynamics in an external radiation field.The result is a quantum electrodynamic formulation in which one works in the Furry picture. The electron field operator in this picture is a solution to the Dirac equation with external field, and is appropriately represented by an expansion in terms of wave packets of Volkov solutions, the latter being exact, explicitly known solutions to the above named equation. The null-plane formulation is required for the consistent construction and implementation of the Volkov wave packets.This formalism permits one to do calculations which take the external field (laser field) into account exactly while treating the quantized photon field (self-field) via the usual perturbation method as adapted to null planes.