Nonlinear Compton scattering in time-dependent electric fields beyond the locally constant crossed field approximation

Locally constant crossed field approximation (LCFA) is a powerful tool for theoretical and numerical studies of various strong field quantum electrodynamical effects. We explore this approximation in detail for photon emission by a spinless particle in a strong time-dependent electric field. This kind of electromagnetic fields is of particular interest, because, in contrast to the comprehensively studied case of a plane wave, they are not crossed. We develop an approach for calculating photon emission probability in a generic time-dependent electric field, establish the range of applicability of LCFA, and calculate the corrections to it.