High Energy Physics, Field Theory, Cosmology, Biophysics, Condensed Matter Physics, Mathematical Physics
Field Theoretical Description of Quantum Systems. Field theory allows us to extract the long distance physics of strongly correlated quantum systems. In particle physics, the long distance field theory is known and people are trying to identify the short distance structure responsible. In condensed matter physics, on the other hand, the physics on the lattice scale is known but one might like to derive the effective long distance field theory and to determine the quantum numbers of the elementary excitations. In recent years, my work has focussed on the application of field theory to the gauge theory of high temperature superconductivity, to the quantum Hall fluids and the double-layered Hall system, and to the theory of random matrices and disordered systems. Many concepts from particle physics, such as gauge theory, topological action, confinement, magnetic monopoles, have all proved to be relevant. The hope is that concepts formulated in our studies of condensed matter systems will in turn enrich our understanding of particle physics.