  Particle production induced by a time-dependent background is well understood
as the projection of the time-evolved initial state onto a set of final states.
While the asymptotic initial and final states are well defined in the usual
way, the definition of particles and antiparticles at intermediate times in the
presence of external fields is ambiguous. These external fields moreover induce
divergences which require regularization. In this paper we clarify some
subtleties in the computation of transient effects in physical quantities for
fermions in a homogeneous axion background, including Schwinger production in
background electromagnetic fields. The presence of the axion requires
particular care as well as knowledge of the UV theory when regulating the
theory and computing the vacuum contribution to the fermion energy.
