Análise da energia de Casimir no cenário de violação de Lorentz do tipo éter com altas derivadas - Dantas, Robson Alves (2023)
In this Dissertation, we study the Casimir effect associated with a quantum, scalar, real and massive field, confined between two parallel plates, in a Lorentz symmetry breaking scenario. The adopted Lorentz violation is a combination of two different symmetry breaking procedures. One is the presence of the constant vector in the context of the aetherlike violation, and the other originates from the Hořava-Lifshtz model, where there is an anisotropy in space-time, with high derivatives in space. We assume that the fields obey the Dirichlet, Neumann and mixed boundary conditions on the plates. For each condition, we calculate the Casimir energy per unit area, assuming that the constant vector is space-like, being parallel and perpendicular to the plates. We show that the modification of the Casimir energy caused by the Lorentz violation depends on the adopted boundary conditions, the direction of the constant vector and the order of the spatial derivative.