Short-distance Schwinger-mechanism and chiral symmetry

In this paper, we study Schwinger pair production of charged massless particles in constant electric fields of finite-extent. Exploiting a map from the Dirac and Klein-Gordon equation to the harmonic oscillator, we find exact pair production rates for massless fermions and scalars. Pair production rates depend only on the ratio between the capacitor plate separation, $\ell$, and the length-scale of the force-field, $\ell_F$. Chirality ensures that fermion production smoothly vanishes with $\ell/\ell_F$. Scalar pair production though diverges exponentially quickly in this limit. The same limit of the smooth tanh-potential does not diverge; divergences seem tied to singularities in current and charge densities.