Sólitons BPS no modelo CP(2) acoplado minimamente com a ação de Maxwell-Chern-Simons

Abstract

The dissertation addresses the study of radial symmetry s olitons in (2+1)-dimensions in a model in which the CP(2)- eld interacts minimally with an Abelian gauge eld ruled by the Maxwell-Chern-Simons term. The implementation of the Bogomol'nyi-Prasad-Sommer eld (BPS) formalism makes possible to nd rst-order di erential equations (BPS equations) whose solutions (BPS states) minimize the total energy of the system. The potential which generates BPS solitons is obtained through a simple but e ective methodology will be shown in detail. The magnetic ux and the total BPS energy are directly proportional to the winding numberg characterizing the non-trivial topology of the solutions, i.e., they are quantized. The analysis of the behavior of the solutions at the boundaries (at the origin and in nite) is performed by solving the linearized BPS equations. Finally, the complete solutions are obtained numerically and the respective pro les are presented which we comment on their main properties.