  We discuss the Schwinger mechanism in scalar QED and derive the multiplicity
distribution of particles created under an external electric field using the
LSZ reduction formula. Assuming that the electric field is spatially
homogeneous, we find that the particles of different momenta are produced
independently, and that the multiplicity distribution in one mode follows a
Bose-Einstein distribution. We confirm the consistency of our results with an
intuitive derivation by means of the Bogoliubov transformation on creation and
annihilation operators. Finally we revisit a known solvable example of
time-dependent electric fields to present exact and explicit expressions for
demonstration.
