Casimir-Polder intermolecular forces in minimal length theories

Abstract

Generalized uncertainty relations are known to provide a minimal length $\hslash \sqrt{\beta }$. The effect of such minimal length in the Casimir-Polder interactions between neutral atoms (molecules) is studied. The first order correction term in the minimal uncertainty parameter is derived and found to describe an attractive potential scaling as $r^{-9}$, as opposed to the well-known $r^{-7}$ long range retarded potential.