This review contains theoretical study of resonant quantum electrodynamics processes in a pulsed laser field. The approximation is examined when the pulse width is considerably greater than the character istic time of wave oscillations. The lepton's interaction with the Coulomb potential of a nucleus and each other is considered in the Born approximation. It is demonstrated that the resonant differential cross section of a process in a pulsed light fields may considerably exceed the corresponding cross section in an absence of a laser field. Results obtained may be experimentally verified by the scientific facilities at the SLAC National Accelerator Laboratory and FAIR (Facility for Antiproton and Ion Research, Darmstadt, Germany) project.

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Resonant spontaneous bremsstrahlung by an electron scattered by a nucleus in the field of a pulsed light wave is theoretically investigated. The approximation is examined when the pulse width is considerably greater than the characteristic time of wave oscillations. The electron interaction with the Coulomb potential of a nucleus is considered in the Born approximation. An analytic expression for the resonant differential cross section of the investigated process was obtained for the range of moderately strong fields. The bremsstrahlung cross section contains a resonant peak. The resonant peak's altitude and width are defined by the external pulsed wave properties. The resonant cross section is studied within the ranges of nonrelativistic, relativistic, and ultrarelativistic electron energies. It is demonstrated that the resonant cross section of spontaneous bremsstrahlung may be several orders of magnitude greater than the corresponding cross section in the absence of an external field. Results obtained may be experimentally verified, for example, by the scientific facilities at the SLAC National Accelerator Laboratory.