Vacuum Energy and Casimir Force in a Presence of Skin-depth Dependent Boundary Condition

The vacuum energy-momentum tensor (EMT) and the vacuum energy corresponding to massive scalar field on ${\mathrm{\Re }}_t\times [0,l]\times {\mathrm{\Re }}^{D-2}$ space-time with boundary condition involving a dimensional parameter ($\delta$) are found. The dependent on the cavity size $l$ Casimir energy $\text{wt}{E}_C$ is a uniquely determinable function of mass $m$, size $l$ and “skin-depth” $\delta$. This energy includes the “bulk” and the surface (potential energy) contributions. The latter dominates when $l\sim \delta$. Taking the surface potential energy into account is crucial for the coincidence between the derivative $-\d \wt E_{C}/\d l$andthe$ll$-componentofthevacuumEMT\mathrm{.}Casimirenergy$\wt E_C$ and the bulk contribution to it are interconnected through Legendre transformation, in which the quantity ${\delta }^{-1}$ is conjugate to the vacuum surface energy multiplied by $\delta$. The surface singularities of the vacuum EMT do not depend on $l$ and, for even $D$, $\delta =0$ or $\mathrm{\infty }$, possess finite interpretation. The corresponding vacuum energy is finite and retains known analytical dependence on the dimension $D$.