Electric Field Decay Without Pair Production: Lattice, Bosonization and Novel Worldline Instantons

• URL: http://arxiv.org/abs/2107.04561v3
• Date: Wed, 30 Mar 2022 18:59:20 GMT
• Title: Electric Field Decay Without Pair Production: Lattice, Bosonization and Novel Worldline Instantons
• Authors: Xu-Yao Hu, Matthew Kleban and Cedric Yu
• Abstract summary: We study the quantum evolution of electric fields when the field points in a compact direction with circumference $L d$ using the massive Schwinger model. We uncover a new and previously unknown set of instantons that result in novel physics that disagrees with all previous estimates.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Electric fields can spontaneously decay via the Schwinger effect, the nucleation of a charged particle-anti particle pair separated by a critical distance $d$. What happens if the available distance is smaller than $d$? Previous work on this question has produced contradictory results. Here, we study the quantum evolution of electric fields when the field points in a compact direction with circumference $L < d$ using the massive Schwinger model, quantum electrodynamics in one space dimension with massive charged fermions. We uncover a new and previously unknown set of instantons that result in novel physics that disagrees with all previous estimates. In parameter regimes where the field value can be well-defined in the quantum theory, generic initial fields $E$ are in fact stable and do not decay, while initial values that are quantized in half-integer units of the charge $E = (k/2) g$ with $k\in \mathbb Z$ oscillate in time from $+(k/2) g$ to $-(k/2) g$, with exponentially small probability of ever taking any other value. We verify our results with four distinct techniques: numerically by measuring the decay directly in Lorentzian time on the lattice, numerically using the spectrum of the Hamiltonian, numerically and semi-analytically using the bosonized description of the Schwinger model, and analytically via our instanton estimate.

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