Quantum Electrodynamics and Renormalization Theory in the Infinite-Momentum Frame

Abstract

Time-ordered perturbation theory evaluated in the infinite-momentum reference frame of Weinberg is shown to be a viable calculational alternative to the usual Feynman graph procedure for quantum electrodynamics. We derive the rules of calculation at infinite momentum, and introduce a convenient method for automatically including $z$ graphs (backward-moving fermion contributions). We then develop techniques for implementing renormalization theory, and apply these to various examples. We show that the $P\ensuremath{\rightarrow}\ensuremath{\infty}$ limit is uniform for calculating renormalized amplitudes, but this is not true in evaluating the renormalization constants themselves. Our rules are then applied to calculate the electron anomalous moment through fourth order and a representative diagram in sixth order. It is shown that our techniques are competitive with the normal Feynman approach in practical calculations. Some implications of our results and connections with the light-cone quantization are discussed.