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 hμν 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 Fc(L)=F0(L˜)/−dethμν, where F0 is the Lorentz-invariant expression, and L˜ is the plate separation rescaled by the component of hμν normal to the plates, L˜=L/−hnn. We also analyze the Casimir stress including finite-temperature corrections. The local behavior of the Casimir energy density is also discussed.
Highlights
The existence of a zero-point vacuum energy is one of the main tenets of the quantum formulation of the laws that we believe govern our Universe
When the boundaries of this delimited spatial domain take the form of two parallel plates, this manifestation of the vacuum fluctuation is known as the Casimir effect [2]
In this Letter we explore the manifestation of the spontaneous breakdown of Lorentz invariance (LI), induced by a constant background tensor, on the Casimir effect for a real massive scalar field between two parallel conductive plates in flat spacetime
Summary
In a Quantum Field Theory (QFT), the presence of fluctuating zero-point fields implies the existence of a non-vanishing macroscopic force between the boundaries that delimit a spatial region [1], due to the difference in the spectrum of quantized field modes inside and outside this region. When the boundaries of this delimited spatial domain take the form of two parallel plates, this manifestation of the vacuum fluctuation is known as the Casimir effect [2]. The Casimir effect stands as a potential handle to distinguish between Lorentz-invariant and Lorentz-violating formulations of QFT. In this Letter we explore the manifestation of the spontaneous breakdown of LI, induced by a constant background tensor, on the Casimir effect for a real massive scalar field between two parallel conductive plates in flat spacetime. Our work provides a generalization of previous studies of LI violation in the Casimir context [37, 38]
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