  We study the trident process in inhomogeneous plane wave background fields.
We obtain compact analytical expressions for all terms in the probability,
including the exchange part, for an arbitrarily shaped plane wave. We evaluate
the probability numerically using complex deformation of lightfront time
integrals and derive various analytical approximations. Our results provide
insights into the importance of the one-step and exchange parts of the
probability relative to the two-step process, and into the convergence to the
locally constant field approximation.

High Energy Physics - Phenomenology;High Energy Physics - Theory