  Laser pulses facilitate multiphoton contributions to the trident pair
production $e_L^- \to e_L^- + e_L^- + e_L^+$ , where the label $L$ indicates a
laser field dressed electron ($e^-$) or positron ($e^+$). We isolate the impact
of the pulse envelope in the trident S matrix element, formulated within the
Furry picture, in leading order of a series expansion in the classical
non-linearity parameter $a_0$. Generally, the Fourier transform of the envelope
carries the information on the pulse length, which becomes an easily tractable
function in the case of a $\cos^2$ pulse envelope. The transition to a
monochromatic laser wave can be handled in a transparent manner, as also the
onset of bandwidth effects for short pulses can be factorized out and studied
separately.

High Energy Physics - Phenomenology