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Vacuum Energy and Casimir Force in a Presence of Skin-depth Dependent Boundary Condition | | S.L. Lebedev
; | | Date: |
25 Mar 2000 | | Journal: | Phys.Atom.Nucl. 64 (2001) 1337-1346; Yad.Fiz. 64 (2001) 1413-1422 | | Subject: | hep-th | | Abstract: | The vacuum energy-momentum tensor (EMT) and the vacuum energy corresponding to massive scalar field on $Re_{t} imes [0,l] imes Re^{D-2}$ space-time with boundary condition involving a dimensional parameter ($delta$) 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" $delta$. 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 $-wt E_{C}/l$ 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 $delta^{-1}$ 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 $infty$, possess finite interpretation. The corresponding vacuum energy is finite and retains known analytical dependence on the dimension $D$. | | Source: | arXiv, hep-th/0003229 | | Services: | Forum | Review | PDF | Favorites | |
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