Locally Constant and Crossed-Field Approximation for Description of the Photon Emission in a Strong Oscillating Electric Field

The process of photon emission by a charged scalar particle (spinless analog of an electron) in a strong spatially homogeneous time-dependent electric field is considered. In the case where the emitting particle is ultrarelativistic and the field strength component oriented perpendicular to the particle motion direction is sufficiently large, the emission probability amplitude can be generally calculated within the locally constant field approximation (LCFA). By an example of a linearly polarized oscillating electric field, the applicability limits of this approximation are analyzed, and its predictions are compared with the results of numerical calculation of the process amplitude using the semiclassical solution of the Klein–Gordon equation in a time-dependent field.