Exact Results in Quantum Theory

Physical systems, also classical ones, can be given an operator algebraic description: observables form a certain type of algebra (a C*-algebra) and states turn out to be given by positive linear functionals on it. I will use this argument, due to F. Strocchi, in order to physically motivate C*-algebras (which in mathematics are canonically introduced via Gelfand-Naimark theorem). These objects play a key role in Connes' spectral formalism of noncommutative geometry, which allows, among other things, for a derivationof the Standard Model lagrangian from simple data. The attempt to path integral quantize noncommutative geometries leads to the concept of random noncommutative geometry. Feasibility, on the other hand, restricts our first attempts to the finite-dimensional arena of "fuzzy geometries" (certain finite-dimensional spectral triples we will properly introduce). The purpose of this talk is to show how random fuzzy geometries are related to random multi-matrices. The results are based on arXiv:1912.13288, which also builds on work by Barrett-Glaser.
Link: https://meet.google.com/sha-kxag-sqx?hs=122