Relativistic quantum particle in a time-dependent homogeneous field

► The problem of the motion of a relativistic quantum particle under the action of a time-dependent force is solved. ► The evolution operator for a definite class of differential and finite-difference equations is constructed. ► The operator identities of Baker-Campbell-Hausdorff type are obtained. ► The time-dependent propagators of the system are computed. ► All expressions have correct non-relativistic and free particle limit.