Local effects of the quantum vacuum in Lorentz-violating electrodynamics

Abstract

The Casimir effect is one of the most remarkable consequences of the non-zero vacuum energy predicted by quantum field theory. In this paper we use a local approach to 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 similar to that used for obtaining the Born series for the scattering amplitudes in quantum mechanics, we compute, at leading order in the Lorentz-violating coefficients, 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 the Green's function. We discuss its structure in the region between the plates. We compute the renormalized vacuum stress, which is obtained as the difference between the vacuum stress in the presence of the plates and that of the vacuum. The Casimir force is evaluated in an analytical fashion by two methods: by differentiating the renormalized global energy density and by computing the normal-normal component of the renormalized vacuum stress. We compute the local Casimir energy, which is found to diverge as approaching the plates, and we demonstrate that it does not contribute to the observable force.

New point-like sources and a conducting surface in Maxwell–Chern–Simons electrodynamics

“…There is also a generalization of the Chern-Simos electrodynamics in 3 + 1 dimensions, the so called Carroll-Field-Jackiw model [37], which exhibits Lorentz symmetry breaking and whose corresponding electrostatics and magnetostatics has been studied thoroughly in reference [38], as well as the Casimir Effect, in references [39,40]. Another coupling involving the dual gauge field strength tensor in 3 + 1 dimensions is the so called axion θ -electrodynamics, which can be used to describe insulators with boundaries [41][42][43][44].…”

New Effects in the Vicinity of a Perfectly Conducting Plate in a Non-minimal Lorentz Violation Scenario

“…From Eq. (47) we can see that the plate is submitted to a force which points in the opposite direction of the projection of the background vector along the unitaryẑ. This kind of effect does not occur in the model studied in ref.…”

“…Defining φ as the angle between the background vector d and theẑ axis, we can write the force (47) in the form…”

Casimir energy and topological mass for a massive scalar field with Lorentz violation

“…In these contexts, Casimir energy has been considered in Refs. [20,21] and [22][23][24], respectively. Therefore, with such a great number of theoretical works, it is natural that the search for Lorentz symmetry violations also acquire experimental interest and, in this sense, the Casimir effect becomes an even more interesting topic to study, since it can be related with Lorentz symmetry violation models.…”