Time-space noncommutativity and Casimir effect

Abstract

We show that the Casimir force and energy are modified in the κ-deformed space-time. This is shown by solving the Green's function corresponding to κ-deformed scalar field equation in presence of two parallel plates, modelled by δ-function potentials. Exploiting the relation between Energy-Momentum tensor and Green's function, we calculate corrections 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.