Strong field induced creation of transverse positron-electron pairs from the vacuum

We investigate the process of electron-positron pair creation from the vacuum in the presence of a static and spatially inhomogeneous electric field. In a common visualization of the Schwinger process, virtual particles are accelerated along the direction of the field's force, transitioning into real particles. Within a nonrelativistic, quantum mechanical framework, a particle cannot gain kinetic energy perpendicular to the external field. However, in the Schwinger mechanism, particles with significant transverse (perpendicular) momenta are predicted. In this study, we analyze the properties of particles with transverse momentum and observe that particles moving rapidly along the field direction (longitudinally) tend to acquire larger transverse momenta. Conversely, positrons with slower longitudinal velocities can only gain small amounts of transverse momentum during their creation.