ar X iv : h ep - t h / 99 12 29 1 v 1 3 1 D ec 1 99 9 Small object limit of Casimir effect and the sign of the Casimir force

We show a simple way of deriving the Casimir Polder interaction, present some general arguments on the finiteness and sign of mutual Casimir interactions and finally we derive a simple expression for Casimir radiation from small accelerated objects. Introduction The purpose of this short paper is threefold: (a)First we show by using direct path integral techniques that the Casimir attraction[1] between objects small relative to their separation does become the celebrated Casimir-Polder interaction[2]. (b) We comment on the sign of casimir forces when the type of the boundary condition is changed and for different geometries. and finally in(c) we find a simple and very suggestive expression for the " Casimir radiation " of such small bodies when these are accelerated. While many of the issues /techniques of this paper have been considered/used before[3, 4] we have some novel, hopefully useful insights and results.