Casimir Force at a Finite Cut-Off

We calculate the Casimir force at a finite cut-off Λ bysumming the forces induced by the all fluctuation modes. We showthat the Casimir force is independent of the cut-off function in thelimit LΛ → ∞. There is a correction in the order of(LΛ)^-2, when LΛ is finite and large. Thiscorrection becomes remarkable when L is comparable with themicroscopic length scaleΛ^-1. It has been demonstrated that the Casimir force at a finite cut-off should be defined bysumming forces of all fluctuation modes, instead of the derivativeof Casimir energy with respect to L where an additional derivativeof the cut-off function has been introduced.