Forma simplética para ondas não-lineares da corda clássica no espaço Ad'S IND.5' - Torres Bejarano, David Alfredo [UNESP] (2013)
In this master thesis we calculate the sympletic form that represents the phase space for a classical nonlinear string in the Anti-de Sitter space (AdS). We review some concepts of di?erential geometry, such as di?erential manifolds, tensor ?elds, dual transformation given by the Hodge star operator 'estrela' and the integration of differential forms on manifolds. We study some applications of these tools in classical mechanics such as the construction of a sympletic manifold, its relation with the phase space, and the Poisson algebra. We show some examples to better understand the theory, such as the case of the nonrelativistic particle, the free scalar ?eld, and the bosonic string given by the Polyakov action. As a motivation for the study of the AdS/CFT correspondece we present the solution for a disturbance of the classical string on the AdS space, which is given by a nonlinear wave on the worldsheet. By calculating the energy of this wave we show that it coincides with the energy radiated by an accelerated charge in the Classical Electrodynamics. Finally, from the found solution, we construct the phase space that describes the classical string on the AdS5