  We study nonperturbative pair production in electric fields with lightlike
inhomogeneities, using complex worldline instantons. We show that the instanton
contribution to the pair production probability is a complex contour integral
over the instanton itself, and that pair production in the considered fields
can be recast in terms of Cauchy's residue theorem. The instantons contribute
residues from the poles they circulate (i.e. give local contributions), and the
invariance of complex integrals under contour deformation manifests in the
instanton contributions as invariance under a set of generalised, complex,
reparameterisations.
