# Casimir pistons with generalized boundary conditions: a step forward

## TL;DR

This paper generalizes the analysis of the Casimir effect in piston geometries by considering all possible boundary conditions for massless scalar fields, using spectral zeta functions and scattering theory.

## Contribution

It introduces a comprehensive framework for calculating Casimir forces with generalized boundary conditions in piston geometries, extending previous specific boundary case studies.

## Key findings

- Explicit Casimir force expressions for spherical and disk manifolds.
- Demonstrates the impact of boundary conditions on Casimir force magnitude.
- Provides a unified approach applicable to various geometries and boundary conditions.

## Abstract

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.