We present a method to obtain soliton solutions to relativistic system of coupled scalar fields. This is done by examining the energy associated to static field configurations. In this case we derive a set of first-order differential equations that solve the equations of motion when the energy saturates its lower bound. To illustrate the general results, we investigate some systems described by polynomial interactions in the coupled fields.Comment: RevTex4, 5 page

We study the equivalence between the self-dual and the Maxwell-Chern-Simons (MCS) models coupled to dynamical, U(1) charged matter, both fermionic and bosonic. This is done through an iterative procedure of gauge embedding that produces the dual mapping of the self-dual vector field theory into a Maxwell-Chern-Simons version. In both cases, to establish this equivalence a current-current interaction term is needed to render the matter sector unchanged. Moreover, the minimal coupling of the original self-dual model is replaced by a non-minimal magnetic like coupling in the MCS side. Unlike the fermionic instance however, in the bosonic example the dual mapping proposed here leads to a Maxwell-Chern-Simons theory immersed in a field dependent medium.

We consider a three-dimensional model of spinor fields with a Thirring-like, quadrilinear selfinteraction. Using either two-or four-component Dirac spinors, we prove that the 1 / N expansion for the model is renormalizable if a gauge structure to select physical quantities is introduced. For certain values of the coupling, the leading 1 / N approximation exhibits bound-state poles. Dynamical breaking of parity or chiral symmetry is shown to occur as a cooperative effect of different orders of 1 / N , if N is smaller than the critical value N,= 1 2 8 / r 2~, where D is two or four depending on whether the fermion field has two or four components.

In this paper we consider a class of systems of two coupled real scalar fields in bidimensional spacetime, with the main motivation of studying classical or linear stability of soliton solutions. Firstly, we present the class of systems and comment on the topological profile of soliton solutions one can find from the first-order equations that solve the equations of motion. After doing that, we follow the standard approach to classical stability to introduce the main steps one needs to obtain the spectra of Schrödinger operators that appear in this class of systems. We consider a specific system, from which we illustrate the general calculations and present some analytical results. We also consider another system, more general, and we present another investigation, that introduces new results and offers a comparison with the former investigations.

We investigate the presence of topological defects inside domain walls in a specific system of coupled real scalar fields. This system belongs to a general class of systems of coupled real scalar fields, and presents some interesting properties in 1ϩ1 dimensions. The potential that identifies the system is defined with two parameters, and we show that this is enough to implement the idea concerning the presence of defects inside defects.