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I read about the Casimir and dynamical Casimir effect. However it is always mentioned in the context of electromagnetism and with two perfectly conducting plates. My question is whether there can be a something like a Casimir Effect for other interactions as well like the strong or weak force.

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It is indeed possible, and in some cases helpful to model Casimir-like effects with other interactions!

It can be hard to model the Casimir effect properly from a more rigorous point of view, because the matter involved in a real-world (or even idealized) conductor is fairly complex, but I have seen models of Casimir-like effects used in quantum field theory for that purpose. This happens in particular for domain walls.

In a field theory, there may be more than one vacuum state (state of lowest energy). This may lead to configurations of fields where the field is in one of the vacuum in one region and another in another region. The number of vacua regions is (in some theories anyway) an invariant, meaning that it is impossible for the field to simply settle to a single vacuum. Therefore, in such cases, there is a transitional region where the field goes from one vacuum to the other. This region is referred to as a domain wall. While typically quite thin, it is not typically an actual surface.

Using various field configurations, it's possible to create a set of several domain walls. A good toy model for this for instance is the scalar field theory

$$\mathcal{L} = \frac{1}{2} \left[ \partial_\mu \phi \partial^\mu \phi + \partial_\mu \psi \partial^\mu \psi + \lambda (\psi^2 - k^2)^2 + m^2(1 - \frac{\psi^2}{k^2}) \phi^2 + g \phi^4 \right]$$

$(\psi^2 - k^2)^2$ is the type of potential to create a domain wall ($\psi$ has a ground state for $\pm k$), while $(1 - \frac{\psi^2}{k^2}) \phi^2$ gives us an interaction between $\psi$ and $\phi$, and $\phi^4$ is your typical self-interaction. In other words, we have a field that can create "walls", which can interact with another field. This can give us a very simplified (at least as far as QFT is concerned) model of the Casimir effect.

It has been shown that such a system does have negative energy density near a single wall. I don't know if more specific configurations with, let's say, two walls or an oscillating wall have been tried, though, to show more Casimir-like effects.

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