Short-distance Schwinger-mechanism and chiral symmetry

TL;DR

This paper derives exact pair production rates for massless particles in finite electric fields, revealing how chirality influences fermion production and highlighting divergences linked to potential singularities.

Contribution

It provides an exact analytical solution for Schwinger pair production in finite electric fields, emphasizing the role of chirality and potential singularities.

Findings

Fermion pair production vanishes smoothly with increasing plate separation.

Scalar pair production diverges exponentially in the same limit.

Divergences are associated with singularities in current and charge densities.

Abstract

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.