Date: Monday, March 27, 2006 Time: 4:00 p.m. Room: Fine Arts B 103 Opening Remarks by Jack Sabin Associate Dean and Director, IT Refreshments: 5:00 p.m. in LIT 339

Abstract:
The idea of particle has been with us since the ancient Greeks (atomos). But it was verified only a century ago through the discovery of the electron, the first item in a long and still growing list of stable elementary systems. In this lecture, a survey is given of our present theoretical understanding of these fundamental constituents of matter.

A first breakthrough was made by Wigner, who proposed to describe particles as irreducible quantum systems whose states transform covariantly under the action of the spacetime symmetries. On the mathematical side, this triggered the theory of induced representations of non-compact groups, and it led to an understanding of the properties of mass and spin. Further progress was made when it was realized that the spacetime localization properties of observational procedures and their causal structure have to be taken into account in the mathematical formalism. This principle of locality is the basis for our present understanding of the appearance of anti-particles, the phenomenon of particle (Bose or Fermi) statistics and global compact symmetry groups (charges). On the mathematical side, these developments required progress in category theory and led to deep duality theorems in the theory of representations of compact groups.

However, they also led to a crisis in our understanding of particles: the prototype of a model of particle physics, quantum electrodynamics, is in conflict with Wigner's particle concept. The nature of this conflict and earlier attempts to circumvent it will be explained. A promising mathematical concept covering all stable particles (and containing Wigner's concept as a special case) is the recent notion of particle weights. It is based on a novel approach to Dirac's old idea of improper states of sharp energy and momentum and involves new tools in functional analysis.

 ^* Professor Detlev Buchholz is one of the world's leading authorities on mathematical quantum field theory. For his theory of scattering of relativistic massless particles, he was awarded the Gustav Hertz Prize of the German Physical Society. Former Chief Editor of Reviews in Mathematical Physics, he also received prizes from the Humboldt Foundation and the Japanese Society for the Promotion of Science.

This lecture is part of the Mathematics Department's Special Year in Probability and Analysis. For more information see the website:

http://qseries.org/~sam/payr/