First-order strong-field QED processes including the damping of particle states

Volkov states are exact solutions of the Dirac equation in presence an arbitrary plane wave. states, as well free photon not stable background plane-wave field but "decay" electrons/positrons can emit photons and transform into electron-positron pairs. By using corresponding Schwinger-Dyson equations within locally-constant approximation, we compute probabilities nonlinear single Compton scattering Breit-Wheeler pair production by including effects decay electron, positron, states. As a result, find that these processes be expressed integral over light-cone time known valid for per unit times time-dependent exponential damping function each interacting particle. The incoming (outgoing) either electron/positron or at corresponds to total probability emits via transforms until (from on). It is interesting terms depend only on particles momentum also their spin (for electrons/positrons) polarization photons). This additional dependence discrete quantum numbers prevents application sum-rules, which significantly simplify computations perturbative regime.