# Dispersion Forces Between Fields Confined to Half Spaces

## TL;DR

This paper models the Casimir effect between scalar fields confined to half spaces, providing a formalism for calculating vacuum energy and exploring interactions akin to photon-matter interactions in slabs.

## Contribution

It introduces a new formalism for calculating the Casimir effect with scalar fields confined to half spaces, including one-loop contributions and renormalization techniques.

## Key findings

- Developed a formalism for vacuum energy calculation in half-space configurations.
- Performed ultraviolet renormalization for the model.
- Calculated one-loop contributions to the wave equation.

## Abstract

We consider the Casimir effect for a scalar field interacting with another scalar field that is confined to two half spaces. This model is aimed to mimic the interaction of the photon field with matter in two slabs. We use Dirichlet boundary conditions on the interfaces for the fields in the half spaces and calculate their one-loop contribution to the wave equation for the other field. We perform the ultraviolet renormalization and develop a convenient formalism for the calculation of the vacuum energy in this configuration.