Quantum fields in low-dimensional systems

Quantum physics in low-dimensional systems has been offered much attention in later years. The reason for this is both the technological aspects and the many unsolved questions concerning the quantum nature of these systems. The present doctoral program i n focussed on questions concerning the application of field theoretical methods to low-dimensional systems. In the first part a mapping from two-dimensional lattice model will be used to study the problem of translational invariance in Mott insulators. Th e second part of the program is devoted to a study of excitations with fractional charge and fractional statistics in a one-dimensioanl Luttinger liquid model. Of particular interest is to relate this to the question of Luttinger liquid behaviour in carbo n nanotubes. The third part concerns the description of many-particle systems that are subject to strong oscillating fields.