Underestimated Schwinger threshold in dimension-reduced approach

Abstract

We perform a large scale of quantum field theoretical simulations in 1+1 spacetime, to examine the Schwinger threshold in a spatially finite-extended electric field. We get a smaller field threshold compared to that introduced by the Schwinger’s formula as well as the worldline instantons. We also check the location-based production rate to show that the boundary effect on the field threshold is limited. At last, we explain the reduced Schwinger threshold in terms of the absence of the transverse momentum in 1-dimensional space, which could make the particle more massive to experience a higher threshold in 3-dimensional space. Our results indicate that the field threshold for the Schwinger effect could be underestimated in 1-dimensional approach which is commonly used in previous studies.