Casimir-Polder potential from first principles

Abstract

The Casimir-Polder potential is introduced in a brief historical discussion ofintermolecular forces. To show how the potential can be found from basic ideasof elementary physics, the interaction energy between two polarizable moleculesis first found in classical electrodynamics when the molecules are bathed in anon-uniform and time-varying external field. This result is then used to findthe Casimir-Polder interaction between the pair by taking the external fieldto be the vacuum field in quantum electrodynamics. An alternative route toobtain the Casimir-Polder potential is outlined. This involves examining thechange in the zero-point energy of the radiation field when two polarizablemolecules are placed within a large empty cavity. Furthermore, it is shown howmany-body forces are endemic in any situation where the forces are mediated bythe electromagnetic Maxwell fields. In particular, the three-body energy shiftsthat occur when three molecules are present is found using the method ofzero-point energy differences.