Quantum Electrodynamics at Infinite Momentum: Scattering from an External Field

TLDR

The incoming electron is viewed as composed of bare Schrödinger-field quanta that interact slowly at high laboratory energies. The study develops a quantum electrodynamics theory in the infinite-momentum frame to describe scattering of energetic electrons or photons off an external field. The formalism treats each bare constituent as independently scattered by the external field, then recombining via perturbative interactions, and is applied to elastic scattering, bremsstrahlung, pair production, and deep-inelastic electro-production using perturbation theory to build initial and final state wave functions. This approach reproduces Cheng and Wu’s results, yields a physical picture that realizes Feynman’s parton model, and successfully describes elastic, bremsstrahlung, pair production, and deep-inelastic processes.

Abstract

Using a formulation of quantum electrodynamics in the infinite-momentum frame, we develop a theory to describe the scattering of energetic electrons or photons off an external field. A physical picture emerges which proves to be a realization of Feymnan's "parton" ideas. In this picture the incoming electron is composed of bare constituents (the quanta of the Schr\"odinger fields) which, at high laboratory energies, interact slowly with one another. Each bare constitutent is scattered from the external field in a simple way and then the constituents again interact among themselves to form the final state. This formalism is applied to elastic electron and photon scattering, bremsstrahlung and pair production, and deep-inelastic electro-production of lepton pairs, and the results of Cheng and Wu and others are recovered in a simple way. In these applications, perturbation theory is used to construct the wave functions of the constituents in the initial and final states.