Instability of a uniform electric field in pure non-Abelian Yang-Mills theory

Abstract

We study the Schwinger process in a uniform non-Abelian electric field using a dynamical approach in which we evolve an initial quantum state for gluonic excitations. We evaluate the spectral energy density and number density in the excitations as functions of time. The total energy density has an ultraviolet divergence which we argue gets tamed due to asymptotic freedom, leading to $g^4E^4t^4$ growth, where $g$ is the coupling and $E$ the electric field strength. We also find an infrared divergence in the number density of excitations whose resolution requires an effect such as confinement.