  Extending work by Gies and Karbstein on the Euler-Heisenberg Lagrangian, it
has recently been shown that the one-loop propagator of a charged scalar
particle in a constant electromagnetic field has a one-particle reducible
contribution in addition to the well-studied irreducible one. Here we further
generalize this result to the spinor case, and find the same relation between
the reducible term, the tree-level propagator and the one-loop Euler-Heisenberg
Lagrangian as in the scalar case. Our demonstration uses a novel worldline path
integral representation of the photon-dressed spinor propagator in a constant
electromagnetic field background.
