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Casimir Effect in $κ$-deformed Theory

Quantum mechanical fluctuations in an interval give rise to the Casimir effect, which destabilizes the size of the interval. This can be problematic in constructing Kaluza-Klein theories. We consider the possibility that a breakdown of the Poincaré symmetry in an extra dimension can solve this instability problem. As a specific example, we consider the space-time with a $κ$-deformed Poincaré algebra, calculate the Casimir force between two plates, and find that we can have an interval with a stable size.