Box Subtraction Scheme in the Anti-Periodic Casimir Energy Calculation for Scalar Field in One Spatial Dimension

In this paper we investigate the Casimir energy for systems with Anti-Periodic Boundary Conditions (BCs) in one spatial dimension by Box Subtraction Scheme (BSS). The BSS is a slight modification of Boyer's subtraction method to remove divergences from expressions in the Casimir energy calculation. The more routine method which involves many regularization and analytic continuation procedures has some ambiguities. These ambiguities have been described recently in some papers. However, in this paper we shall investigate some of them and also we describe the main ingredient of the BSS in the subtraction of two comparable configurations for our problem. Usually, two approaches in the Leading order Casimir energy are yield identical results but the latter regularization has more manifest way to remove divergences from expressions. So it could be the best instrument for us to remove complicated divergences which appear in the higher order radiative corrections to the Casimir energy. Extracting and obtaining of finite results from complicated divergent expressions without resorting to any analytic continuation techniques is also the other privilege of the BSS. In this paper we use this regularization method to obtain the Casimir energy and in final we compare our results with those reported in the literature, which are obtained from other regularization techniques.