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The influence of quantized electromagnetic fields on a nonrelativisticcharged particle moving near a conducting plate is studied. We give afield-theoretic derivation of the nonlinear, non-Markovian Langevin equation ofthe particle by the method of Feynman-Vernon influence functional. Thisstochastic approach incorporates not only the stochastic noise manifested fromelectromagnetic vacuum fluctuations, but also dissipation backreaction on acharge in the form of the retarded Lorentz forces. Since the imposition of theboundary is expected to anisotropically modify the effects of the fields on theevolution of the particle, we consider the motion of a charge undergoingsmall-amplitude oscillations in the direction either parallel or normal to theplane boundary. Under the dipole approximation for nonrelativistic motion,velocity fluctuations of the charge are found to grow linearly with time in theearly stage of the evolution at the rather different rate, revealing stronganisotropic behavior. They are then asymptotically saturated as a result of thefluctuation-dissipation relation, and the same saturated value is found for themotion in both directions. The observational consequences are discussed. planeboundary. Velocity fluctuations of the charge are found to grow linearly withtime in the early stage of the evolution at the rate given by the relaxationconstant, which turns out to be smaller in the parallel case than in theperpendicular one in a similar configuration. Then, they are asymptoticallysaturated as a result of the fluctuation-dissipation relation. For theelectron, the same saturated value is obtained for motion in both directions,and is mainly determined by its oscillatory motion. Possible observationalconsequences are discussed.

Stochastic Lorentz forces on a point charge moving near the conducting plate