Casimir Force at a Finite Cut-Off

摘要: We calculate the Casimir force at a finite cut-off Lambda by summing the forces induced by the all fluctuation modes. We show that the Casimir force is independent of the cut-off function in the limit L Lambda -> infinity. There is a correction in the order of (L Lambda)(-2), when L Lambda is finite and large. This correction becomes remarkable when L is comparable with the microscopic length scale Lambda(-1). It has been demonstrated that the Casimir force at a finite cut-off should be defined by summing forces of all fluctuation modes, instead of the derivative of Casimir energy with respect to L where an additional derivative of the cut-off function has been introduced.