  Early-time electron-positron correlation in vacuum pair-production in an
external field is investigated. The entangled electron and positron wave
functions are obtained analytically in the configuration and momentum spaces.
It is shown that, relative to that of the one-dimensional theory, two- and
three-dimensional calculations yield enhanced spatial correlation and broadened
momentum spectrum. In fact, at early times the electron and positron almost
coincide spatially. The correlation also depends on the direction of the
applied field. For the spatial correlation, the transverse correlation is
stronger than the longitudinal one.
