Resonant quantum electrodynamics processes proceeding in strong pulsed light fields, realized in modern powerful pulsed lasers is presented. The resonant character relates to the fact that lower-order processes, such as spontaneous emission and one-photon creation and annihilation of electron-positron pairs, may be allowed in the field of a light wave. Therefore, within a certain range of energy and momentum, a particle in an intermediate state may fall within the mass shell. The resonant peak's altitude and width are defined by the external pulsed wave properties. It is demonstrated that the resonant cross sections may be several orders of magnitude greater than the corresponding cross sections in the absence of an external field. Results obtained may be experimentally verified, for example, by the scientific facilities at sources of pulsed laser radiation (SLAC, FAIR, XFEL, ELI, XCELS).

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