Feynman's propagator for a charged particle with time-dependent mass in a crossed time-varying electromagnetic field.

Abstract

Through a sequence of time-dependent transformations and time substitution, we evaluate the propagator of a harmonically bound charged particle with time-dependent mass in a time-varying electromagnetic field by relating it to those of free particles. From this propagator we derive the wave functions. The propagators beyond and at caustics are then investigated, respectively, by including the Maslov phase factor and by using the modified semigroup property. Finally, we calculate explicitly the propagator for the constant-damping case.