Estudo do efeito Casimir com violação de Lorentz do tipo éter - Cruz, Messias de Brito (2019)
The Quantum Gravity theories, such as String Theory and Loop Quantum Gravity, predict the possibility of a spontaneous violation of the Lorentz symmetry. Because of this fact, the interest by the violation of Lorentz symmetry has grown rapidly in recent decades because it could be a way of testing the candidate theories for Quantum Gravitation. Motivated by models of Quantum Field Theory with Lorentz violations etherlike, we have analyzed the influence of a Lorentz violation on the Casimir effect, assuming that the quantum fields are confined between two parallel plates. Initially, we analyzed the Casimir effect at zero temperature, using a model for massive scalar fields with Lorentz violation of the etherlike. Considering different boundary conditions for the scalar field in the plates, we obtained the Casimir energy and pressure for different choices of the constant 4-vector that implements a anisotropy at space-time. Then, as a natural extension, we consider the effects of finite temperature. For each choice of the 4-vector, we obtained the thermal correction of the Casimir energy per unit area. We note that the violation of the Lorentz symmetry has a strong influence on the scalar Casimir effect, especially when the constant 4-vector is orthogonal to the plates. Subsequently, we analyzed the Casimir effect at zero temperature, through a model for massive fermionic fields with Lorentz violation of the etherlike. In this study, we imposed to the fermionic field the MIT bag boundary condition on the plates, considering different choices for the constant 4-vector, which implements an anisotropy at space-time. For the timelike 4-vector we observe that the Lorentz violation does not modify the Casimir energy. However, for the situation that the 4-vector is spacelike, the Lorentz violation has a significant influence on the fermionic Casimir effect. We obtained explicitly the Casimir energy per unit area for the case of the 4-vector is orthogonal to the plates and, consequently, the Casimir pressure. Thus, the Casimir effect would be a good candidate to investigate a supposed violation of Lorentz symmetry.