  The process of nonlinear electron-positron pair production by an electron
colliding with an arbitrary plane wave electromagnetic field (nonlinear trident
pair production) is studied analytically and numerically. Special emphasis is
put on the properties of the transition amplitude. In fact, its original
expression as resulting from applying the Wick's theorem turns out to be
divergent and not to manifestly fulfill gauge invariance. By restoring the
latter, the amplitude is regularized and investigated in different regimes. In
particular, the amplitude is divided into a two-step and a one-step
contributions, depending on the scaling dependence on the laser pulse duration.
The corresponding contributions to the positron angular distribution spectra
and the resulting interference terms are studied numerically emphasizing the
possibility of measuring experimentally the contribution of the one-step
contribution.
