Friday, November 3, 2006
Chern-Simons, Anyon? Why Knot?
Physics Department, Cal Poly Pomona
For the past two decades or so, Chern-Simons theory provided an amazing framework for the confluence of topology, topological quantum field theory, and condensed matter physics. Mathematically, it extends the Chern classes as powerful topological and differential-geometric tools, and physically, it serves as the basis for effective quantum field theories capable of describing systems of quasiparticles obeying fractional (other than Fermi-Dirac or Bose-Einstein) statistics—the so-called anyons. An important physical application is to the fractional quantum Hall effect. Its diverse physical applications underlines a modern basic theme in theoretical physics: the deep connection between topology and physics. This is spectacularly demonstrated by the Chern-Simons-Witten theory, where the calculation of the vacuum expectation values of the Wilson loops, physical observables directly related to the Bohm-Aharonov and the more general geometric (Berry) phases, miraculously yields various sophisticated topological invariants of knots and links embedded in 3-dimensional manifolds (such as the Jones polynomials). The latter are distinctly mathematical objects whose characterization had baffled mathematicians for more than a century! In this talk I will (presumptuously) try to provide an overview of some of the above topics, from a lay person's perspective.
Refreshments at 4:00 PM. Seminar begins at 4:10 PM.
Building 8 (Science Bldg.) - Room 241
For further information, please call (909) 869-4014