A non-perturbative approach to the scalar Casimir effect with Lorentz symmetry violation

Abstract

We determine the effect of Lorentz invariance violation in the vacuum energy and stress between two parallel plates separated by a distance $L$, in the presence of a massive real scalar field. We parametrize the Lorentz-violation in terms of a symmetric tensor $h^{\mu \nu }$ that represents a constant background. Through the Green's function method, we obtain the global Casimir energy, the Casimir force between the plates and the energy density in a closed analytical form without resorting to perturbative methods. With regards to the pressure, we find that ${\mathcal{F}}_c(L)={\mathcal{F}}_0(\tilde{L})/\sqrt{-\det h^{\mu \nu }}$, where ${\mathcal{F}}_0$ is the Lorentz-invariant expression, and $\tilde{L}$ is the plate separation rescaled by the component of $h^{\mu \nu }$ normal to the plates, $\tilde{L}=L/\sqrt{-h^{nn}}$. We also analyze the Casimir stress including finite-temperature corrections. The local behavior of the Casimir energy density is also discussed.

6 pages, No figures

References in corpus (7)

• Casimir Effect confronts Cosmological Constant
• Energy-momentum tensor of a Casimir apparatus in a weak gravitational field: scalar case
• Recent measurements of the Casimir force: Comparison between experiment and theory
• Acceleration of the Universe driven by the Casimir force
• Constraints on axion and corrections to Newtonian gravity from the Casimir effect
• Gravitation of the Casimir Effect and the Cosmological Non-Constant
• Quantum field theory with dynamical boundary conditions and the Casimir effect

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