Classical and quantum symmetries in models of dimensionally reduced gravity

Dimensional reduction of various gravity and supergravity models leads to effectively two-dimensional field theories described by gravity coupled nonlinear G/H coset space #sigma#-models. This thesis is devoted to an analysis of these models within the canonical framework, exploiting the close relations to well-known integrable field theories. A complete set of conserved nonlocal charges is derived from the transition and monodromy matrices of the associated linear system. Their Poisson algebra is a modified (twisted) version of the semi-classical Yangian double. The classical infinite-dimensional symmetry group (the Geroch group) is generated by the Lie-Poisson action of these charges. The structures completely extend to models with local supersymmetry, taking into account all additional fermionic degrees of freedom. Canonical quantization of the algebra of charges leads to a twisted Yangian double with fixed central extension at a critical level. The last chapter collects some results within the so-called isomonodromic approach to these models. (orig.)Available from TIB Hannover: RR 8919(1998-034) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman