Abstract
We discuss quantum-mechanical many-body systems interacting with a topological field, known as topological quantum fields. Several topics on the theory of quantum fluids are examined. First we establish the existence of topological gauge fields in high-T c superconductors and in Heisenberg quantum antiferromagnets. Then we consider typical topological quantum fluids, known as quantum Hall fluids, which are systems exhibiting the fractional quantum Hall effect (FQHE). A theoretical model of these fluids is described in detail. We also discuss the long distance physics of topological quantum fluids, their topological order parameter and possible experimental tests of the theory.
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