  General formulation in the realm of strong-field quantum electrodynamics is
provided for a process that occurs in the presence of a train of laser pulses
and, in the tree level, is represented by a two-vertex Feynman diagram with
exchange of a virtual photon. A scheme of retrieving resonances in the
corresponding probability distributions is also formulated in these general
settings. While the presented formalism is applicable to a variety of processes
like electron-positron pair creation and annihilation, M\"oller scattering,
Bhabha scattering, etc., we illustrate it for a trident process. Specifically,
we consider electron-positron pair creation in the muon--laser-field
collisions. We demonstrate that the probability distributions exhibit
integrable singularities close to the threshold of pair creation. Also, a
variety of resonances is observed that originate from the poles of the Feynman
photon propagator. While those resonances are, in general, obscured by strong
quantum interferences, we show that they can be isolated by changing the
carrier envelope phase of the driving laser pulses. In that case, while
transformed into the Lorentz-Breit-Wigner shape profile, the resonance position
and width can be determined.
