  We show how all possible one-particle reducible tadpole diagrams in constant
electromagnetic fields can be constructed from one-particle irreducible
constant-field diagrams. The construction procedure is essentially algebraic
and involves differentiations of the latter class of diagrams with respect to
the field strength tensor and contractions with derivatives of the one-particle
irreducible part of the Heisenberg-Euler effective Lagrangian in constant
fields. Specific examples include the two-loop addendum to the Heisenberg-Euler
effective action as well as a novel one-loop correction to the charged particle
propagator in constant electromagnetic fields discovered recently. As an
additional example, the approach devised in the present article is adopted to
derive the tadpole contribution to the two-loop photon polarization tensor in
constant fields for the first time.
