# Time-space noncommutativity and Casimir effect

## TL;DR

This paper investigates how kappa-deformation of space-time alters the Casimir effect, deriving corrections to the force and energy, and constraining the deformation parameter based on experimental data.

## Contribution

It provides a detailed calculation of Casimir force modifications in kappa-deformed space-time up to second order in the deformation parameter.

## Key findings

- Casimir force receives corrections scaling as L^{-4} and L^{-6}
- Corrections produce attractive forces
- Deformation parameter constrained below 10^{-23} meters

## Abstract

We show that the Casimir force and energy are modified in the kappa-deformed space-time. This is analysed by solving the Green's function corresponding to kappa-deformed scalar field equation in presence of two parallel plates, modelled by delta-function potentials. Exploiting the relation between energy-momentum tensor and Green's function, we calculate the correction to Casimir force, valid up to second order in the deformation parameter. The Casimir force is shown to get corrections which scale as $L^{-4}$ and $L^{-6}$ and both these types of corrections produce attractive forces. Using the measured value of Casimir force, we show that the deformation parameter should be below $10^{-23}$m.