A non-perturbative approach to the scalar Casimir effect with Lorentz symmetry violation - C.A. Escobar; A. Martín-Ruiz; O.J. Franca; Marcos A. G. Garcia (Physics Letters B, 2020)
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.