Vacuum fluctuation and retardation effects on long-range potentials

The Casimir-Polder R^-7 retarded potential between two neutral (polarizable) atoms at a separation R, which replaces the nonrelativistic R^-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^-5 potential between a charged point particle and a polarizable system—an addition to the usual R^-4 polarization potential—and the R^-3 two-photon contribution to the potential between two charged point particles. It also suggests a new, R^-2 potential—an addition to the usual R^-1 image potential—between a charged point particle and a conducting wall.