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The specific features of nonlinear pair production and radiation processes inan ultratsrong rotating electric field are investigated, taking into accountthat this field models the antinodes of counterpropagating laser beams. It isshown that a particle in a rotating electric field acquires an effective masswhich depends on its momentum absolute value as well as on its direction withrespect to the field plane. This phenomenon has an impact on the nonlinearBreit-Wheeler and nonlinear Compton processes. The spectra of the producedpairs in the first case, and the emitted photon in the second case, are shownto bear signatures of the effective mass. In the first case, the threshold forpair production by a $\gamma$-photon in the presence of this field variesaccording to the photon propagation direction. In the second case, varying theenergy of the incoming electron allows for the measurement of the momentumdependence of the effective mass. Two corresponding experimental setups aresuggested.

Nonlinear QED in an ultrastrong rotating electric field: Signatures of the momentum-dependent effective mass