Feynman Rules and Quantum Electrodynamics at Infinite Momentum

Abstract

We have studied the Feynman rules in terms of the new variables $s=p^0-p^3$, $\eta =p^0+p^3$, $\mathrm{q}=(p^1, p^2)$ in the ${\phi }^3$ model and in quantum electrodynamics. The connection between the new variables and the dynamics at infinite momentum is established. In the ${\phi }^3$ model, one easily deduces Weinberg's rules at infinite momentum upon integrating over the $s$ variables in the propagators without taking the $p^3\to \infty$ limit. The new Feynman rules lead to much simpler calculation of the second-order self-energies and the magnetic moment in quantum electrodynamics. It is still unclear if there is advantage in computing higher-order terms in quantum electrodynamics with the new rules.