Schwinger effect in compact space: a real time calculation

Abstract

We compute the discharging rate of a uniform electric field due to Schwinger pair production in $(1+1)$-dimensional scalar electrodynamics with a compact dimension of radius $R$. Our calculation is performed in real time, using the in-in formalism. For large compactification radii, $R\to \infty$, we recover the standard non compact space result. However, other ranges of values of $R$ and of the mass $m$ of the charged scalar give rise to a richer set of behaviors. For $R\gtrsim \mathcal{O}(1/m)$ with $m$ large enough, the electric field oscillates in time, whereas for $R\to 0$ it decreases in steps. We discuss the origin of these results.

13 pages, 5 figures

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Cited by in corpus (5)

• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• Electric Field Decay Without Pair Production: Lattice, Bosonization and Novel Worldline Instantons
• Roles of electric field/time-dependent Wilson line in toroidal compactification with or without magnetic fluxes
• Kaluza-Klein Schwinger effect
• Schwinger Effect in Compact Space