Deformando geometricamente o modelo 𝝓^4 generalizado

Abstract

This work aims to study topological field configurations in the one-dimensional scalar theories, i.e., kink- and antikink-like solutions. We begin by presenting a review of classical field theory, which addresses some fundamental concepts such as spontaneous symmetry breaking, solitons, and topological charges. Subsequently, one presents Bogomol’nyi-Prasad-Sommerfield (BPS) formalism, which enables the derivation of stable topological solutions through first-order BPS equations. Posteriorly, this formalism is then employed to investigate solutions from the 𝝓^4 and Sine-Gordon models. Furthermore, extensions of the 𝝓^4 theory via a generalized kinetic term (also referred to as a noncanonical theory) are studied. Our main contribution is the proposal of a modified model, constructed using a hyperbolic generalization that breaks the ℤ_2 symmetry. The study concludes with an analysis of the topological solutions emerging from the hyperbolically generalized 𝝓^4 model and its linear excitation spectrum. The results demonstrate the viability of the proposed model and open new avenues for research in effective field theories, as well as potential applications in physical systems with softly broken translational symmetry.