The Casimir energy for scalar field with mixed boundary condition

Abstract

In this study, the first-order radiative correction to the Casimir energy for massive and massless scalar fields confined with mixed boundary conditions (BCs) (Dirichlet–Neumann) between two points in [Formula: see text] theory was computed. Two issues in performing the calculations in this work are essential: to renormalize the bare parameters of the problem, a systematic method was employed, allowing all influences from the BCs to be imported in all elements of the renormalization program. This idea yields our counterterms appeared in the renormalization program to be position-dependent. Using the Box Subtraction Scheme (BSS) as a regularization technique is the other noteworthy point in the calculation. In this scheme, by subtracting the vacuum energies of two similar configurations from each other, regularizing divergent expressions and their removal process were significantly facilitated. All the obtained answers for the Casimir energy with the mixed BC were consistent with well-known physical grounds. We also compared the Casimir energy for massive scalar field confined with four types of BCs (Dirichlet, Neumann, mixed of them and Periodic) in [Formula: see text] dimensions with each other, and the sign and magnitude of their values were discussed.