Novel results for kinklike structures and their connections to quantum mechanics

Abstract

In this work we use the deformation procedure and explore the route to obtain distinct field theory models that present similar stability potentials. Starting from systems that interact polynomially or hyperbolically, we use a deformation function which allows to construct other theories having the feature of giving rise to the same stability potentials. Such deformation function leads to smooth potentials according to a specific choice of a single parameter. Among the results, one shows that for models with asymmetric topological sectors, the appearance of a new stability potential is also possible.

Kink scattering in hyperbolic models

“…On the contrary, one can reconstruct a field theory from some characteristic of a quantum mechanical potential [47][48][49][50]. In [51], the authors review some results about the deformation procedure in systems with a single real scalar field [51][52][53] that give rise to distinct field theories having the same stability potential. In their work, several models with polynomial and hyperbolic interactions were considered.…”

A novel connection between scalar field theories and quantum mechanics

“…In this sense, the works in Refs. [32,33] introduce several models of real scalar fields with a diversity of topological sectors, and we are now examining how to deform them to obtain new families of models with similar quantum mechanics [34]. We have done the same with the sine-Gordon model, but since it is periodic and supports an infinite number of equivalent topological sectors, we have gotten nothing new, because adding a finite number of topological sectors to it does not change the model itself.…”

Explicit kinks in higher-order field theories

“…Despite some certainly interesting attempts to obtain explicit expressions for kinks of models with polynomial potentials [15,51] with very specific set of vacua, kinks of the ϕ 8 model and of higher degree models so far could mainly be obtained in the implicit form. The purpose of this paper is to show that in some more general cases (for some relations between model parameters) it is possible to obtain explicit formulae for kinks.…”

“…and Until now, it was believed that kinks of the ϕ 8 model can be obtained only in an implicit form, i.e., in the form of the dependence x = x(ϕ) (apparently with the exception of a particular case [51]). However, as we will demonstrate below, a detailed analysis of the solutions of the static equation of motion shows that, at least for particular values of the ratio b/a, kinks can be obtained in the explicit form ϕ = ϕ(x).…”