Casimir effect in 2+1 dimensional noncommutative theories

Abstract

We study the Dirichlet Casimir effect for a complex scalar field on two noncommutative spatial coordinates plus a commutative time. To that end, we introduce Dirichlet-like boundary conditions on a curve contained in the spatial plane, in such a way that the correct commutative limit can be reached. We evaluate the resulting Casimir energy for two different curves: (a) Two parallel lines separated by a distance $L$, and (b) a circle of radius $R$. In the first case, the resulting Casimir energy agrees exactly with the one corresponding to the commutative case, regardless of the values of $L$ and of the noncommutativity scale $\theta$, while for the latter the commutative behaviour is only recovered when $R>>\sqrt{\theta }$. Outside of that regime, the dependence of the energy with $R$ is substantially changed due to noncommutative corrections, becoming regular for $R\to 0$.

12 pages, 3 figures

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• How does Casimir energy fall in $\kappa$-deformed space-time?
• Centripetal force on Casimir energies in $\kappa$-deformed rotating frame
• Dirichlet boundary conditions in a noncommutative theory