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Electron-positron pair production in spatially and temporally inhomogeneouselectric and magnetic fields is studied within the Dirac-Heisenberg-Wignerformalism (quantum kinetic theory) through computing the corresponding Wignerfunctions. The focus is on discussing the particle momentum spectrum regardingsignatures of Schwinger and multiphoton pair production. Special emphasis isput on studying the impact of a strong dynamical magnetic field on the particledistribution functions. As the equal-time Wigner approach is formulated interms of partial integro-differential equations an entire section of themanuscript is dedicated to present numerical solution techniques applicable toWigner function approaches in general.

On the effect of time-dependent inhomogeneous magnetic fields on the particle momentum spectrum in electron-positron pair production