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 ${g}^{4}{E}^{4}{t}^{4}$ 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.
Highlights
The Schwinger effect [1], whereby nonperturbative quantum effects in a background electric field lead to electron-positron pair production, has received much attention
The exponential suppression of the original Schwinger effect is not present, and other techniques have to be employed as pair creation is no longer a tunneling process that is exponentially suppressed
The result is surprising to us since the Schwinger process can be viewed as a tunneling process and one might expect that the Wentzel-Kramers-Brillioun (WKB) [23,24] and other approximations used to obtain (1) would break down for massless gauge fields
Summary
The Schwinger effect [1], whereby nonperturbative quantum effects in a background electric field lead to electron-positron pair production, has received much attention (for example, see the reviews [2,3,4,5,6]). The result is surprising to us since the Schwinger process can be viewed as a tunneling process and one might expect that the Wentzel-Kramers-Brillioun (WKB) [23,24] and other approximations used to obtain (1) would break down for massless gauge fields For this reason we wish to reexamine the problem using a different approach. (For a kinetic approach to QED, see [25,26,27,28,29,30].) At the initial time, we consider a color electric field background and quantum excitations in their noninteracting ground state.
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