Análise da equação de Klein-Gordon em sistemas astrofísicos compactos - Lourenço, Roger Eduardo (2023)
In this work, we focus on demonstrating that any twist in 1+1 dimensions can be directly obtained from a scalar field that is a solution of a firstorder linear differential equation with constant coefficients. This is achieved through an appropriate field transformation. We elicit and delve into several models, analyzing how the introduction of an underlying scalar field can open up new possibilities in models involving a scalar field. The general approach is presented and discussed, along with some compelling arguments and important physical applications. This approach, for certain parameter values, exhibits symmetry breaking like the 4 model. For other parameter values, it corresponds to a model with no minima, resulting in kink configurations for the scalar field. This is accomplished through a convenient field transformation that satisfies a linear differential equation for the transformation function. We extract and delve into several models and propose a novel method through potential deformation.