  Non-perturbative electron-positron pair creation (Schwinger effect) is
studied based on the equal-time Wigner formalism in 1+1 dimensions. An ab
initio calculation of the Schwinger effect in the presence of a simple space-
and time-dependent electric field pulse is performed for the first time,
allowing for the calculation of the time evolution of observable quantities
such as the charge density, the particle number density or the total number of
created particles. We predict a new self-bunching effect of charges in phase
space due to the spatial and temporal structure of the pulse.
