Colloquium: Tuesday, May 15, 2 pm. Speaker: Daniel Sternheimer (Keio University). Title: “The reasonable effectiveness of mathematical deformation theory in physics”.
New fundamental physical theories can, so far a posteriori, be seen as emerging from existing ones via some kind of deformation. That is the basis for Flato’s “deformation philosophy”, of which the main paradigms are the physics revolutions from the beginning of the twentieth century, quantum mechanics (via deformation quantization) and special relativity. On the basis of these facts we explain how symmetries of hadrons (strongly interacting elementary particles) could “emerge” by deforming in some sense (including quantization) the Anti de Sitter symmetry (AdS), itself a deformation of the Poincaré group of special relativity. The ultimate goal is to base on fundamental principles the dynamics of strong interactions, which originated over half a century ago from empirically guessed “internal” symmetries. We start with a rapid presentation of the physical (hadrons) and mathematical (deformation theory) contexts, including a possible explanation of photons as composites of AdS singletons and of leptons as similar composites. Then we present a “model generating” framework in which AdS would be deformed and quantized (possibly at root of unity and/or in manner not yet mathematically developed with noncommutative “parameters”). That would give (using deformations) a space-time origin to the “internal” symmetries of elementary particles, on which their dynamics were based, and either question, or give a conceptually solid base to, the Standard Model, in line with Einstein’s quotation: “The important thing is not to stop questioning. Curiosity has its own reason for existing.”