Dynamical Properties of one dimensional Mott Insulators

At low energies the charge sector of one dimensional Mott insulators can be described in terms of a quantum Sine-Gordon model. Using exact results derived from integrability it is possible to determine dynamical properties like the frequency dependent optical conductivity. We compare the exact results to perturbation theory and renormalisation group calculations. We also discuss the application of our results to experiments on quasi-1D organic conductors.Comment: 17 pages, 5 figures, to appear in the proceedings of the NATO ASI/EC summer school "New Theoretical Approaches to Strongly Correlated Systems" Newton Institute for Mathematical Sciences, Cambridge UK, April 200

Quantization of Midisuperspace Models

We give a comprehensive review of the quantization of midisuperspace models. Though the main focus of the paper is on quantum aspects, we also provide an introduction to several classical points related to the definition of these models. We cover some important issues, in particular, the use of the principle of symmetric criticality as a very useful tool to obtain the required Hamiltonian formulations. Two main types of reductions are discussed: those involving metrics with two Killing vector fields and spherically symmetric models. We also review the more general models obtained by coupling matter fields to these systems. Throughout the paper we give separate discussions for standard quantizations using geometrodynamical variables and those relying on loop quantum gravity inspired methods.Comment: To appear in Living Review in Relativit