Colloque des sciences mathématiques du Québec

22 septembre 2006 de 16 h 00 à 18 h 00 (heure de Montréal/HNE) Sur place

Quantum Mechanics, the Stability of Matter, and Quantum Electrodynamics

Colloque par Elliott Lieb (Princeton University)

Ordinary matter is held together with electromagnetic forces, and the dynamical laws governing the constituents (electrons and nuclei) are those of quantum mechanics. These laws, found in the beginning of this century, were able to account for the fact that electrons do not fall into the nuclei and thus atoms are quite robust. It was only in 1967 that Dyson and Lenard were able to show that matter in bulk was also stable and that two stones had a volume twice that of one stone. Simple as this may sound, the conclusion is not at all obvious and hangs by a thread-- namely Pauli's "exclusion principle" (which requires that for N electrons one must consider only the N-fold antisymmetric product of L^2(R^3) instead of the full product). In the ensuing 3 decades much was accomplished to clarify, simplify and extend this result. We now understand that matter can, indeed, be unstable when relativistic effects and magnetic fields are taken into account -- unless the electron's charge is small enough (which it is, fortunately). These delicate and non-intuitive conclusions will be summarized. The requisite mathematical apparatus needed for these results is itself interesting. Finally, we can now hope to begin an analysis of the half-century old question about the ultimate theory of ordinary matter, called quantum electrodynamics (QED). This is an experimentally successful theory, but one without a decent mathematical foundation. Some recent, preliminary steps in resolving the infinities of QED will be presented.


UQAM, Pav. Sherbrooke, 200, rue Sherbrooke O., salle SH-3420