具有广义边界条件的Casimir活塞：向前的一步
Casimir pistons with generalized boundary conditions: a step forward
摘要：
本文研究了$I\times N$型活塞几何中传播的无质量标量场的Casimir效应，其中$I$是实数线的区间，$N$是光滑紧致黎曼流形.我们的分析代表了一个概括的活塞配置，因为我们认为所有可能的边界条件，被允许施加在标量场上获得的结果。在散射理论的框架内，我们采用谱zeta函数形式，得到了活塞上的Casimir能量和相应的Casimir力的表达式。当流形$N$是$d$维球面和圆盘时，我们给出了Casimir力的显式结果.
英文摘要：
In this work we study the Casimir effect for massless scalar fields propagating in a piston geometry of the type $I\times N$ where $I$ is an interval of the real line and $N$ is a smooth compact Riemannian manifold. Our analysis represents a generalization of previous results obtained for pistons configurations as we consider all possible boundary conditions that are allowed to be imposed on the scalar fields. We employ the spectral zeta function formalism in the framework of scattering theory in order to obtain an expression for the Casimir energy and the corresponding Casimir force on the piston. We provide explicit results for the Casimir force when the manifold $N$ is a $d$-dimensional sphere and a disk.
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