Non-perturbative methods in non-linear field theories and their supersymmetric extensions

Zusammenfassung

The principal goal of this Ph.D. thesis is a deeper study on non-linear field theories relevant in high energy physics, using concepts of K field and supersymmetry. The concept on non-linearity is related with the fact that a lot of interesting theories like Skyrme model, Skyrme-Faddev model (model for QCD at low energies), baby Skyrme, etc. have higher power in the kinetic terms (the so-called K field theories). These theories allow us to find solutions with different properties with respect to the standard situation, like for example solutions with compact support (compactons). However they are really interesting in cosmology for the study of the inflationary epoch. Supersymmetric extensions of K field theories are interesting because, in one hand supersymmetry is seen as a fundamental symmetry of the natures, and then, it is interesting itself, and in the other hand, it is a powerful tool in the analysis of non-linear field theories. The supersymmetric versión of such theories allow to calculate BPS type solutions or topological charges.