与反德西特时空边界正交的枝蔓上的表面卡西米尔密度

Physics Pub Date : 2023-09-12 DOI:10.3390/physics5040074
A. Saharian
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摘要

本文研究了在与反德西特(AdS)时空边界正交的两个支链几何中,具有一般曲率耦合的标量场的表面能动张量(SEMT)的真空期望值。对于支链上的罗宾边界条件,SEMT 被分解为与支链自能相对应的贡献和由第二支链的存在引起的部分。只有第一部分需要重正化,相应的正则化采用广义zeta函数法。诱导的 SEMT 是有限的,不存在重正化歧义。对于生活在星云上的观测者来说,相应的状态方程属于宇宙常数类型。根据边界条件和支链之间的间隔,表面能量密度可以是正的,也可以是负的。在德里赫特和诺伊曼边界条件的特殊情况下,磁链上的诱导能量密度会消失。引力对诱导的 SEMT 的影响,在各支链之间的距离达到或大于 AdS 时空的曲率半径时是至关重要的。在相当大的分离极限中,作为适当分离的函数,SEMT 的衰减对于无质量场和大质量场都遵循幂律。对于闵科夫斯基体中的平行板和大质量场,相应期望值的衰减是指数式的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Surface Casimir Densities on Branes Orthogonal to the Boundary of Anti-De Sitter Spacetime
The paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes and the parts induced by the presence of the second brane. The renormalization is required for the first parts only, and for the corresponding regularization the generalized zeta function method is employed. The induced SEMT is finite and is free from renormalization ambiguities. For an observer living on the brane, the corresponding equation of state is of the cosmological constant type. Depending on the boundary conditions and on the separation between the branes, the surface energy densities can be either positive or negative. The energy density induced on the brane vanishes in special cases of Dirichlet and Neumann boundary conditions on that brane. The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime. In the considerably large separation limit, the decay of the SEMT, as a function of the proper separation, follows a power law for both massless and massive fields. For parallel plates in Minkowski bulk and for massive fields the fall-off of the corresponding expectation value is exponential.
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