Aspectos de integrabilidade do modelo de Thirring acoplado

Abstract

This dissertation investigates aspects of integrability in (1+1)-dimensional field theories, with emphasis on the coupled Thirring model. Initially, the foundations of classical integrability are presented, including Liouville integrability, the zero-curvature formalism, and Bäcklund transformations. Subsequently, the sine-Gordon model and the massive Thirring model are analyzed from the perspective of their integrable structures. The main focus of this work lies on the coupled Grassmannian Thirring model, in which the Lax connection based on the superalgebra 𝑠𝑙(2, 1) is explicitly constructed, ensuring the classical integrability of the system. The Bäcklund transformations are generalized and the permutability property is analyzed, allowing for the systematic construction of multiparametric solutions. It is noteworthy that the explicit attainment of these multiparametric solutions for the coupled model constitutes a novel result in the literature. It is expected that such solutions are related to N-soliton solutions of the bosonic version of the coupled model.