Al-Khwarizmi
Applied Mathematics Webinar 

Next talk (Special Session): March 31, 2026. 

Tuesday - 5:00 pm (KSA)- (2:00 pm GMT) 

Zoom link: https://ksu-hub.zoom.us/j/97753107489

Speaker:   Luigi Accardi, University of Rome, Italy. 

Title: Probabilistic Quantization in Applied Mathematics 

Abstract: The emergence of Heisenberg commutation rule [q, p] = iℏ for position and momentum in boson quantum mechanics (QM), and more generally of non–commutativity in QM, has been a mystery since the dawn of this theory and has remained so for almost 100 years. The discovery of the quantum decomposition of a classical random variable gave rise to a line of research that, in little more that 25 years, has produced a natural solution to this problem, namely: the whole quantum theory (QT) can be deduced from the combination of classical probability (CP) with the classical theory of orthogonal polynomials (OP). The importance of this new approach does not lie so much in the solution of the problem mentioned above, as in the fact that the QT used until now appears as a very special case of a much broader purely deductive theory, which shows that every classical random variable with all moments, is canonically associated to a new QT, which reduces to the standard boson one in the case of gaussian random variables and to the standard fermion one in the case of Bernoulli random variables. That’s why we speak of probabilistic quantization. In other words, for the first time in almost 100 years, the mathematical apparatus of QT appears in the perspective of a natural deduction and not as a strange, singular theory justified a posteriori by its enormous empirical success, but totally mysterious in its origins and meaning. The fruitfulness of this new point of view is demonstrated by the fact that it has already led to the solution of several open problems in classical probability, in the classical theory of orthogonal polynomials and in physics itself, where it has provided powerful new tools for the description of natural phenomena. This poses an exciting challenge for everybody interested in classical probability and its applications. In fact, since we now know that quantization is a universal classical probabilistic phenomenon and that every classical random variable with all moments (or process or field, since the theory applies also to infinite dimensions) canonically produces a quantum theory, it follows that every field of science in which classical probability is involved (i.e. almost all), will have to learn how to exploit the benefits of this duality between classical and quantum description. By exploiting the quantum mathematical formalism, the physicists have managed to produce fantastic results in the past 100 years: now this power is available to all those who use classical probability in any field of science and technology. We need to learn to use these new mathematical tools.