Lectures on Non Perturbative Field Theory and Quantum Impurity Problems

H. Saleur

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Lectures on Non Perturbative Field Theory and Quantum Impurity Problems

H. Saleur

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Abstract

These are lectures presented at the Les Houches Summer School ``Topology and Geometry in Physics'', July 1998. They provide a simple introduction to non perturbative methods of field theory in 1+1 dimensions, and their application to the study of strongly correlated condensed matter problems - in particular quantum impurity problems. The level is moderately advanced, and takes the student all the way to the most recent progress in the field: many exercises and additional references are provided. In the first part, I give a sketchy introduction to conformal field theory. I then explain how boundary conformal invariance can be used to classify and study low energy, strong coupling fixed points in quantum impurity problems. In the second part, I discuss quantum integrability from the point of view of perturbed conformal field theory, with a special emphasis on the recent ideas of massless scattering. I then explain how these ideas allow the computation of (experimentally measurable) transport properties in cross-over regimes. The case of edge states tunneling in the fractional quantum Hall effect is used throughout the lectures as an example of application.

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H. Saleur. 1998-12-07. Lectures on Non Perturbative Field Theory and Quantum Impurity Problems. https://arxiv.org/abs/cond-mat/9812110

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