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arXiv · 0711.4272

Casimir effect in 2+1 dimensional noncommutative theories

C. D. Fosco·G. A. Moreno
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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 $θ$, while for the latter the commutative behaviour is only recovered when $R >> \sqrtθ$. Outside of that regime, the dependence of the energy with $R$ is substantially changed due to noncommutative corrections, becoming regular for $R \to 0$.

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C. D. Fosco, G. A. Moreno. 2007-11-27. Casimir effect in 2+1 dimensional noncommutative theories. https://doi.org/10.1016/j.physletb.2007.12.015

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