Schwinger pair production at nonzero temperatures or in compact directions

TL;DR

This paper calculates the rate of Schwinger pair production at nonzero temperatures and in compact directions, revealing new instantons that significantly enhance decay rates through combined thermal and quantum effects.

Contribution

It introduces a novel instanton framework that accounts for thermal fluctuations and compact geometries, improving understanding of electric field decay mechanisms.

Findings

High-temperature decay dominated by a new instanton involving thermal fluctuation and quantum tunneling.

Decay in small compact circles involves a process reducing the electric field without producing charged particles.

Decay rates are exponentially faster than previously estimated in the literature.

Abstract

Electric fields may decay by quantum tunneling: as calculated by Schwinger, an electron-positron pair may be summoned from the vacuum. In this paper I calculate the pair-production rate at nonzero temperatures. I find that at high temperatures the decay rate is dominated by a new instanton that involves both thermal fluctuation and quantum tunneling; this decay is exponentially faster than the rate in the literature. I also calculate the decay rate when the electric field wraps a compact circle (at zero temperature). The same new instanton also governs this rate: I find that for small circles decay is dominated by a process that drops the electric field by one unit, but does not produce charged particles.