Efeito Casimir para o campo escalar com violação das simetrias de Lorentz no formalismo TFD

Abstract

The main objective of this work is to describe the Casimir effect for a massive scalar field through a formalism known as Thermo Field Dynamics (TFD), in the presence of a term that is responsible for violating Lorentz symmetries. The Casimir effect is a quantum phenomenon that involves the attraction of neutral, conducting plates placed parallel to each other, subjected to a perfect vacuum. Such an effect was predicted in 1948 and proved in the laboratory in 1958. Lorentz symmetries is considered a fundamental symmetry of nature that, in principle, there should be no way to violate it. However, studies that seek a fundamental theory that describes all forces of nature indicate that Lorentz symmetries can be violated and, if observed in our universe, implies the existence of a new physical theory. The TFD formalism is a quantum theory of real-time fields at finite temperature. This formalism describes phenomena having as ground state the thermal vacuum |0(β)i. Quantum phenomena are described in the thermal Hilbert space HT , which is composed of the usual Hilbert space H and the tilde or dual Hilbert space He. Topological effects are introduced through the compactification of one or more space-time dimensions. Compactifing the temporal dimension gives us temperature effects, while compactifing the spatial dimensions gives us size effects. The TFD formalism will be used to calculate the Casimir effect at zero temperature, the Stefan-Boltzmann law and the Casimir effect at finite temperature with the presence of an aether term, responsible for violating the Lorentz symmetries, for different directions of the constant vector u µ.