Abstract
The Casimir effect is one of the most remarkable consequences of the nonzero vacuum energy predicted by quantum field theory. In this contribution we study the Lorentz-violation effects of the minimal standard-model extension on the Casimir force between two parallel conducting plates in the vacuum. Using a perturbative method, we compute the relevant Green’s function which satisfies given boundary conditions. The standard point-splitting technique allow us to express the vacuum expectation value of the stress-energy tensor in terms of this Green’s function. Finally, we study the Casimir energy and the Casimir force paying particular attention to the quantum effects as approaching the plates.
Highlights
Interest in Lorentz violation has grown rapidly in the last decades since many candidate theories of quantum gravity [1, 2], such as string theory [3, 4] and loop quantum gravity [5, 6, 7], possess scenarios involving deviations from Lorentz symmetry
We study the Casimir effect (CE) between two parallel conducting plates using a local approach based on the calculation of the vacuum expectation value of the stress-energy tensor via Green’s functions satisfying the suitable boundary conditions
Vacuum stress-energy tensor In section 2 we gave the stress-energy tensor (SET) for this theory and we showed that it can be written as the sum of two terms: Θμν = T μν + Ξμν
Summary
Interest in Lorentz violation has grown rapidly in the last decades since many candidate theories of quantum gravity [1, 2], such as string theory [3, 4] and loop quantum gravity [5, 6, 7], possess scenarios involving deviations from Lorentz symmetry. We study the Casimir effect (CE) between two parallel conducting plates using a local approach based on the calculation of the vacuum expectation value of the stress-energy tensor via Green’s functions satisfying the suitable boundary conditions. Zhukovsky [18], they used misinterpreted equations which led to an oversimplified treatment of the problem They considered that the photon dispersion relation corresponds to that for a massive photon; unlike the (2+1)D case, in (3+1)D the effect of the Maxwell-Chern-Simons term is a more complicated dispersion relation for the photon. Due to this wrong equation, Frank and Turan constructed incorrectly the relevant Green’s function (GF). Details about this investigation were recently published in Ref. [20]
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