Estudo do efeito Casimir e geração da massa topológica via potencial efetivo em cenários com e sem violação da invariância de Lorentz

Abstract

In this work, the e¤ective potential approach in quantum field theory is used in order to investigate self-interaction loop correction to the Casimir energy density and generation of topological mass for both massless and massive real scalar fiels, which obey a helix type boundary condition. In addition, it is also considered a CPT-even aether-type violation of the Lorentz symmetry, where CPT stands for the symmetries of charge conjugation, parity or space inversion and time reversal, respectively. In the absence of the Lorentz violation, we obtain analytical expressions for the loop correction to the Casimir energy density and to the mass of the scalar field. Afterwards, we consider the same system taking into account the CPT-even aether-type violation, in each spacetime direction and we analyse its e¤ect in the Casimir energy density and also in the topological mass generated. The obtained results are shown in graphics. Besides, we also consider a system of interacting quantum fields, which consists of a real scalar field and a complex field. The interaction considered here is the quartic one, which is a product of the modulus square of the complex field and the square of the real field. It is included the self- interaction associated with each field. In this theory, the scalar field is constrained to obey periodic condition while the complex field obeys in one case a quasiperiodic condition and in other case mixed boundary conditions. In addition to the loop corrections to the Casimir energy density and the topological mass, an analysis of the possible di¤erent stable vacuum states and the corresponding stability condition is also provided. Our results, for this system, are also shown in graphics.