Casimir effect for mixed fields

TL;DR

This paper investigates the Casimir effect for mixed scalar fields confined in a one-dimensional region, revealing that mixing signatures appear only when considering flavor vacuum states, not mass eigenstates.

Contribution

It introduces two approaches to compute the Casimir force for mixed fields and shows that mixing effects are only present in the flavor vacuum framework.

Findings

Mixing signatures appear only in the flavor vacuum approach.

Casimir force calculations differ between mass and flavor representations.

Results are independent of mixing parameters in the mass basis.

Abstract

We analyze the Casimir effect for a flavor doublet of mixed scalar fields con- fined inside a one-dimensional finite region. In the framework of the unitary inequivalence between mass and flavor representations in quantum field theory, we employ two alternative approaches to derive the Casimir force: in the first case, the zero-point energy is evaluated for the vacuum of fields with definite mass, then similar calculations are performed for the vacuum of fields with defi- nite flavor. We find that signatures of mixing only appear in the latter context, showing the result to be independent of the mixing parameters in the former.