Abstract: |
Deformations in physics and mathematics are part of a deformation philosophy, promoted in mathematical physics in joint work with Moshe Flato since the 70's (the notion itself can be traced back to Pythagoras). The main conceptual advances in 20th century physics, relativity and quantization, manifest it. In deformation quantization (including its realization on manifolds), quantization is understood as deformations of commutative algebra structures into non commutative algebra structures (which includes quantum groups). One may also think of objects dual to noncommutative algebras, the so-called quantum spaces, as deformations of classical spaces, the objects dual to commutative algebras (that is the essence of noncommutative geometry). Deforming Minkowski space-time leads to a fruitful object which together with its group of symmetries is referred as AdS or "anti de Sitter space". The study of AdS has significant physical consequences. One example is that massless particles in 4-dimensional space-time like photons become, in a way compatible with quantum electrodynamics, composites of massless particles in 3-dimensional space-time (singletons) that exhibit AdS/CFT correspondence. Combining all this leads to an ongoing program in which AdS would be quantized in some regions related to black holes. We speculate that this could explain a universe in accelerated expansion and maybe baryogenesis. The first part will present the major ideas and the second develop the points which the audience will prefer. It is hoped that this broad picture, "tailor made" for IPMU, will inspire some of its researchers. |