Campos escalares e método da deformação

Abstract

This dissertation constitutes a study on Classical Field Theory, with a specific approach for scalar fields. Initially, the equations of motion, the energy, and the stability conditions of the solutions are presented. These solutions which present topological features are, called kinks, besides the non-topological ones are, named lumps. Moreover, important models are going to be discussed, for instance, models f4, f6, sine-Gordon and double sine-Gordon. The phenomenon of spontaneous symmetry breaking, the Bogomol’nyi method, and the construction of Field Theory based on potentials of quantum mechanics also are going to be addressed. Subsequently, the deformation method is presented, which allows us to build analytic Field Theory models. Finally, we proceed with the application of the method, to obtain new families of sine-Gordon models, and polynomial potentials, that allow are to explore long-range interactions between kinks.