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This work focuses on the analysis of the Casimir effect for pistons subjectto transmittal boundary conditions. In particular we consider, as pistonconfiguration, a direct product manifold of the type $I\times N$ where $I$ is aclosed interval of the real line and $N$ is a smooth compact Riemannianmanifold. By utilizing the spectral zeta function regularization technique, wecompute the Casimir energy of the system and the Casimir force acting on thepiston. Explicit results for the force are provided when the manifold $N$ is a$d$-dimensional ball.

The Casimir effect for pistons with transmittal boundary conditions