Electric field decay without pair production: lattice, bosonization and novel worldline instantons

A bstract 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 ∈ 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.