Vacuum fluctuation and retardation effects on long-range potentials

Abstract

The Casimir-Polder ${R}^{\ensuremath{-}7}$ retarded potential between two neutral (polarizable) atoms at a separation $R$, which replaces the nonrelativistic ${R}^{\ensuremath{-}6}$ van der Waals potential for $R$ sufficiently large, has been derived both by standard techniques and by assuming the atoms to be within a large volume with conducting walls and considering vacuum-fluctuation effects. The latter technique is here used to provide simple derivations of the ${R}^{\ensuremath{-}5}$ potential between a charged point particle and a polarizable system---an addition to the usual ${R}^{\ensuremath{-}4}$ polarization potential---and the ${R}^{\ensuremath{-}3}$ two-photon contribution to the potential between two charged point particles. It also suggests a new, ${R}^{\ensuremath{-}2}$ potential---an addition to the usual ${R}^{\ensuremath{-}1}$ image potential---between a charged point particle and a conducting wall.