Publications (3)0 Total impact
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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 $\theta$, 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 $R \to 0$.
12/2007;
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ABSTRACT: We study the UV properties, and derive the explicit form of the one-loop effective action, for a noncommutative complex scalar field theory in 2+1 dimensions with a Grosse-Wulkenhaar term, at the self-dual point. We also consider quantum effects around non-trivial minima of the classical action which appear when the potential allows for the spontaneous breaking of the U(1) symmetry. For those solutions, we show that the one-loop correction to the vacuum energy is a function of a special combination of the amplitude of the classical solution and the coupling constant.
11/2007;
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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 . Outside of that regime, the dependence of the energy with R is substantially changed due to noncommutative corrections, becoming regular for R→0.
Physics Letters B.
