The infinite mass limit of the two-particle Green's function in QED

TL;DR

This paper investigates the behavior of the two-particle Green's function in QED when one particle's mass approaches infinity, revealing factorization properties and the bound state spectrum consistent with the Dirac equation, and ruling out certain abnormal solutions.

Contribution

It demonstrates that in the infinite mass limit, the two-particle Green's function simplifies and aligns with the Dirac equation, excluding abnormal solutions predicted by ladder approximation.

Findings

Green's function factorizes with infinite mass

Bound state spectrum matches Dirac equation

Excludes abnormal solutions in the limit

Abstract

The behavior of the two-particle Green's function in QED is analyzed in the limit when one of the particles becomes infinitely massive. It is found that the dependences of the Green's function on the relative times of the ingoing and outgoing particles factorize and that the bound state spectrum is the same as that of the Dirac equation with the static potential created by the heavy particle. The Bethe-Salpeter wave function is also determined in terms of the Dirac wave function. The present result excludes the existence, in the above limit, of abnormal solutions due to relative time excitations as predicted by the Bethe-Salpeter equation in the ladder approximation.