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Particle production induced by a time-dependent background is well understoodas 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 usualway, the definition of particles and antiparticles at intermediate times in thepresence of external fields is ambiguous. These external fields moreover inducedivergences which require regularization. In this paper we clarify somesubtleties in the computation of transient effects in physical quantities forfermions in a homogeneous axion background, including Schwinger production inbackground electromagnetic fields. The presence of the axion requiresparticular care as well as knowledge of the UV theory when regulating thetheory and computing the vacuum contribution to the fermion energy.

Transient phenomena in the axion assisted Schwinger effect