Casimir effect in Lorentz-violating scalar field theory: a local approach

Abstract

We study the Casimir effect in the classical geometry of two parallel conductive plates, separated by a distance $L$, for a Lorentz-breaking extension of the scalar field theory. The Lorentz-violating part of the theory is characterized by the term $\lambda {\left(u\cdot \partial \varphi \right)}^2$, where the parameter $\lambda$ and the background four-vector $u^{\mu }$ codify Lorentz symmetry violation. We use Green's function techniques to study the local behavior of the vacuum stress-energy tensor in the region between the plates. Closed analytical expressions are obtained for the Casimir energy and pressure. We show that the energy density ${\mathcal{E}}_C$ (and hence the pressure) can be expressed in terms of the Lorentz-invariant energy density ${\mathcal{E}}_0$ as follows \begin{align} \mathcal{E}_{C} (L) = \sqrt{\frac{1-λu_{n} ^{2}}{1 + λu ^{2}}} \mathcal{E}_{0} (\tilde{L}) , \notag \end{align} where $\tilde{L}=L/\sqrt{1-\lambda u_n^2}$ is a rescaled plate-to-plate separation and $u_n$ is the component of $\vec{u}$ along the normal to the plates. As usual, divergences of the local Casimir energy do not contribute to the pressure.

arXiv comment13 pages, 2 figures, Accepted for publication in PRD

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