Field theory, topology and condensed matter physics. Proceedings of the ninth Chris Engelbrecht summer school in theoretical physics held at Storms River Mouth, Tsitsikamma National Park, South Africa, 17-28 January 1994
This is a series of introductory courses devoted to problems of condensed matter physics for which some nonperturbative methods of the quantum field theory may be applicable. These methods are based on some fundamental concepts having symmetry and topological character. Main subjects touched in the lectures are enumerated below. 1) Renormalization group, scale and conformal invariance in two-dimensional statistical mechanics. 2) Several problems in the statistical mechanics of two-dimensional random surfaces and membranes. 3) Statistical mechanics of one-dimensional objects and polymers and their critical properties. 4) Problems connected with self-avoiding surfaces. 5) Matrix models and strings in low dimensions, their connection with Yang-Mills theory. Construction of a continuum field describing the dynamics of observable loop variables. 6) Topological quantum fluids (essentially quantum Hall fluids). Effective field theory approach to the Hall fluids. Duality, topological order in quantum Hall system. Magnetic monopoles and multi-layered Hall systems. The topological quantity related to orbital spin. Topological orders and edge excitations in fractional quantum Hall liquids. Hydrodynamic approach to the edge excitations and its connection with the effective theory of fractional quantum Hall states. 7) Topological mechanism of superconductivity. Topological instability in strongly correlated electronic systems. Connection of the topological fluid model with canonical Hubbard model.
topological order in quantum Hall system
scientific article; zbMATH DE number 809536