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arXiv · hep-th/0003229

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

S. L. Lebedev
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Abstract

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

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S. L. Lebedev. 2000-03-25. Vacuum Energy and Casimir Force in a Presence of Skin-depth Dependent Boundary Condition. https://doi.org/10.1134/1.1389563

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