2007/11/27 by C. D. Fosco, G. A. Moreno, Gustavo A. Moreno
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Casimir effect #Commutative property #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Noncommutative geometry #Physics #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #RADIUS #Scalar field #hep-th
paper · pdf · doi:10.1016/j.physletb.2007.12.015
published as Phys.Lett.B659:901-905,2008 · 12 pages, 3 figures
arxiv created 2007/11/27 · openalex publication_date 2008/01/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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≫θ. Outside of that regime, the dependence of the energy with R is substantially changed due to noncommutative corrections, becoming regular for R→0.