Tópicos em Defeitos Topológicos: Colisões e Localização de Campos

Abstract

In this work it is introduced a new class of topological defects in (𝐷,1)-dimensions dubbed 𝑝−balls. The defects are constructed, in the absence of gravitational interaction, by ℳ ≥ 1 scalar fields depending radially of 𝑝 spatial dimensions, with 2 ≤ 𝑝 ≤ 𝐷 − 1. It is shown that the defects are stable under radial and angular perturbations. It is analyzed in full generality the issue of localization of a spin−0 particle in the defects. One particle is described by a scalar field Φ sufficiently weak in order not to disturb the defect configuration. The field Φ is attached to the defect by a coupling term in the Lagrangian. After a convenient decomposition of Φ, it is verified that the radial amplitude obeys a Schrödinger-like equation. From this it is possible to investigate numerically the existence of bound or resonant states. Particularizing, are considered examples with one, two and three scalar fields, trying to investigate the way the defect structure, number of radial dimensions and coupling constant between the fields, are related to the occurrence of such states. Next it is studied the localization of spin−1/2 particles in 𝑝−balls generated by two scalar fields in (3,1) dimensions. It is considered a general Yukawa coupling between the defect and the fermionic field as 𝜂𝐹(𝜑,𝜒)𝜓𝜓¯ . Finally it is investigated the dynamics of kink(𝐾) - antikink(𝐾¯ ) collisions between a in twin models. Two twin models are characterized, when static solutions are considered, by the same scalar field and energy density profile. It is determined the way the spectrum of linear excitations around the solutions are responsible by the structure of 𝐾𝐾¯ collisions in twin models from the 𝜑 4 theory.