Charged particle in a time-dependent electric field: A White Noise functional approach

The propagator for a charged particle in a time-dependent electric field is calculated following Hida and Streit's framework [1] where the propagator is the T-transform of Feymnan functional. However, we have to regard the potential V -qE(tau)x root m/n xi x following C.C. Bernido and MX Caipio-Bernido's [2] prescription of time-dependent potentials. The result agrees with the limiting form of Eqn(16) of N.Morgenstern Horing, H.L.Cui, and G. Fiorenza [3], when the magnetic field is switched off, and Eqn(17) of [3] when the electric field is constant in time.