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.

在这项工作中，我们研究了无质量标量场在\（I \ timesN \）类型的活塞几何中传播的卡西米尔效应，其中I是实线的间隔，N是光滑的紧凑黎曼流形。我们的分析代表了对活塞配置所获得的先前结果的概括，因为我们考虑了允许施加在标量场上的所有可能的边界条件。我们在散射理论的框架中采用谱zeta函数形式，以获得卡西米尔能量和相应的卡西米尔作用在活塞上的力的表达式。当流形N为d维球体和圆盘时，我们为卡西米尔力提供了明确的结果。